Accurate prediction of chemical shifts for aqueous protein structure on "Real World" data

Accurate Prediction of NMR Chemical Shifts: Integrating DFT Calculations with Three-Dimensional Graph Neural Networks

Computer prediction of NMR chemical shifts plays an increasingly important role in molecular structure assignment and elucidation for organic molecule studies. Density functional theory (DFT) and gauge-including atomic orbital (GIAO) have established a framework to predict NMR chemical shifts but often at a significant computational expense with a limited prediction accuracy. Recent advancements in deep learning methods, especially graph neural networks (GNNs), have shown promise in improving the accuracy of predicting experimental chemical shifts, either by using 2D molecular topological features or 3D conformational representation. This study presents a new 3D GNN model to predict 1H and 13C chemical shifts, CSTShift, that combines atomic features with DFT-calculated shielding tensor descriptors, capturing both isotropic and anisotropic shielding effects. Utilizing the NMRShiftDB2 data set and conducting DFT optimization and GIAO calculations at the B3LYP/6-31G(d) level, we prepared the NMRShiftDB2-DFT data set of high-quality 3D structures and shielding tensors with corresponding experimentally measured 1H and 13C chemical shifts. The developed CSTShift models achieve the state-of-the-art prediction performance on both the NMRShiftDB2-DFT test data set and external CHESHIRE data set. Further case studies on identifying correct structures from two groups of constitutional isomers show its capability for structure assignment and elucidation. The source code and data are accessible at https://yzhang.hpc.nyu.edu/IMA.

The conformational landscape of fold-switcher KaiB is tuned to the circadian rhythm timescale

How can a single protein domain encode a conformational landscape with multiple stably-folded states, and how do those states interconvert? Here, we use real-time and relaxation-dispersion NMR to characterize the conformational landscape of the circadian rhythm protein KaiB from Rhodobacter sphaeroides . Unique among known natural metamorphic proteins, this variant of KaiB spontaneously interconverts between two monomeric states: the "Ground" and "Fold-switched" (FS) state. KaiB in its FS state interacts with multiple binding partners, including the central KaiC protein, to regulate circadian rhythms. We find that KaiB itself takes hours to interconvert between the Ground and KaiC binding-competent FS state, underscoring the ability of a single protein sequence to encode the slow process needed for its biological function. We reveal that the rate-limiting step between the Ground and FS state is the cis-trans isomerization of three prolines in the C-terminal fold-switching region by demonstrating acceleration of interconversion by the prolyl cis/trans isomerase CypA. The interconversion proceeds through a "partially disordered" (PD) state, where the N-terminal half remains stably folded while the C-terminal half becomes disordered. We discovered two additional properties of KaiB's landscape: firstly, the Ground state experiences cold denaturation: at 4°C, the PD state becomes the majorly populated state. Secondly, the Ground state exchanges with a fourth state, the "Enigma" state, on the millisecond timescale. We combine AlphaFold2-based predictions and NMR chemical shift predictions to suggest that this "Enigma" state represents a beta-strand register shift that eases buried charged residues in the Ground state. These results provide mechanistic insight in how evolution can design a single sequence that achieves specific timing needed for its function.

Significance Statement

One can conceptualize KaiB as an on-off switch to regulate circadian rhythms in bacteria, where the "On state" is the Fold-switched state that binds KaiC and other proteins, and the "Off state" is the Ground state, whose primary function is to not be in the "On state". Our work exemplifies how evolution tuned the kinetics of interconversion to align with the hour-long timescale of its biological function. The Ground state is dramatically destabilized at cold temperatures, and the system contains an alternate "off" conformation that exchanges with the primary "off" conformation at faster timescales than the rate-limiting step. Furthermore, our findings demonstrate a simple principle for evolving a protein switch: one part of a protein domain remains stably folded to serve as a scaffold for the rest of the protein to re-fold.

Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning

Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification of molecules in gas, solution, and solid-state phases. However, accurate prediction of chemical shifts using the gold-standard coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] method with a complete basis set (CBS) can be prohibitively expensive. By contrast, machine learning (ML) methods offer inexpensive alternatives for chemical shift predictions but are hampered by generalization to molecules outside the original training set. Here, we propose several new ideas in ML of the chemical shift prediction for H, C, N, and O that first introduce a novel feature representation, based on the atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics (QM) method, and train it to predict NMR chemical shieldings of a high-level composite theory that approaches the accuracy of CCSD(T)/CBS. In addition, we train the ML model through a new progressive active learning workflow that reduces the total number of expensive high-level composite calculations required while allowing the model to continuously improve on unseen data. Furthermore, the algorithm provides an error estimation, signaling potential unreliability in predictions if the error is large. Finally, we introduce a novel approach to keep the rotational invariance of the features using tensor environment vectors (TEVs) that yields a ML model with the highest accuracy compared to a similar model using data augmentation. We illustrate the predictive capacity of the resulting inexpensive shift machine learning (iShiftML) models across several benchmarks, including unseen molecules in the NS372 data set, gas-phase experimental chemical shifts for small organic molecules, and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.

Biomolecular NMR in the AI-assisted structural biology era: Old tricks and new opportunities

Over the last 40 years nuclear magnetic resonance (NMR) spectroscopy has established itself as one of the most versatile techniques for the characterization of biomolecules, especially proteins. Given the molecular size limitations of NMR together with recent advances in cryo-electron microscopy and artificial intelligence-assisted protein structure prediction, the bright future of NMR in structural biology has been put into question. In this mini review we argue the contrary. We discuss the unique opportunities solution NMR offers to the protein chemist that distinguish it from all other experimental or computational methods, and how it can benefit from machine learning.

The 100-protein NMR spectra dataset: A resource for biomolecular NMR data analysis

Multidimensional NMR spectra are the basis for studying proteins by NMR spectroscopy and crucial for the development and evaluation of methods for biomolecular NMR data analysis. Nevertheless, in contrast to derived data such as chemical shift assignments in the BMRB and protein structures in the PDB databases, this primary data is in general not publicly archived. To change this unsatisfactory situation, we present a standardized set of solution NMR data comprising 1329 2-4-dimensional NMR spectra and associated reference (chemical shift assignments, structures) and derived (peak lists, restraints for structure calculation, etc.) annotations. With the 100-protein NMR spectra dataset that was originally compiled for the development of the ARTINA deep learning-based spectra analysis method, 100 protein structures can be reproduced from their original experimental data. The 100-protein NMR spectra dataset is expected to help the development of computational methods for NMR spectroscopy, in particular machine learning approaches, and enable consistent and objective comparisons of these methods.

Time-optimized protein NMR assignment with an integrative deep learning approach using AlphaFold and chemical shift prediction

Chemical shift assignment is vital for nuclear magnetic resonance (NMR)-based studies of protein structures, dynamics, and interactions, providing crucial atomic-level insight. However, obtaining chemical shift assignments is labor intensive and requires extensive measurement time. To address this limitation, we previously proposed ARTINA, a deep learning method for automatic assignment of two-dimensional (2D)-4D NMR spectra. Here, we present an integrative approach that combines ARTINA with AlphaFold and UCBShift, enabling chemical shift assignment with reduced experimental data, increased accuracy, and enhanced robustness for larger systems, as presented in a comprehensive study with more than 5000 automated assignment calculations on 89 proteins. We demonstrate that five 3D spectra yield more accurate assignments (92.59%) than pure ARTINA runs using all experimentally available NMR data (on average 10 3D spectra per protein, 91.37%), considerably reducing the required measurement time. We also showcase automated assignments of only 15N-labeled samples, and report improved assignment accuracy in larger synthetic systems of up to 500 residues.

Biomolecular NMR spectroscopy in the era of artificial intelligence

Biomolecular nuclear magnetic resonance (NMR) spectroscopy and artificial intelligence (AI) have a burgeoning synergy. Deep learning-based structural predictors have forever changed structural biology, yet these tools currently face limitations in accurately characterizing protein dynamics, allostery, and conformational heterogeneity. We begin by highlighting the unique abilities of biomolecular NMR spectroscopy to complement AI-based structural predictions toward addressing these knowledge gaps. We then highlight the direct integration of deep learning approaches into biomolecular NMR methods. AI-based tools can dramatically improve the acquisition and analysis of NMR spectra, enhancing the accuracy and reliability of NMR measurements, thus streamlining experimental processes. Additionally, deep learning enables the development of novel types of NMR experiments that were previously unattainable, expanding the scope and potential of biomolecular NMR spectroscopy. Ultimately, a combination of AI and NMR promises to further revolutionize structural biology on several levels, advance our understanding of complex biomolecular systems, and accelerate drug discovery efforts.

MIM-ML: A Novel Quantum Chemical Fragment-Based Random Forest Model for Accurate Prediction of NMR Chemical Shifts of Nucleic Acids

We developed a random forest machine learning (ML) model for the prediction of 1H and 13C NMR chemical shifts of nucleic acids. Our ML model is trained entirely on reproducing computed chemical shifts obtained previously on 10 nucleic acids using a Molecules-in-Molecules (MIM) fragment-based density functional theory (DFT) protocol including microsolvation effects. Our ML model includes structural descriptors as well as electronic descriptors from an inexpensive low-level semiempirical calculation (GFN2-xTB) and trained on a relatively small number of DFT chemical shifts (2080 1H chemical shifts and 1780 13C chemical shifts on the 10 nucleic acids). The ML model is then used to make chemical shift predictions on 8 new nucleic acids ranging in size from 600 to 900 atoms and compared directly to experimental data. Though no experimental data was used in the training, the performance of our model is excellent (mean absolute deviation of 0.34 ppm for 1H chemical shifts and 2.52 ppm for 13C chemical shifts for the test set), despite having some nonstandard structures. A simple analysis suggests that both structural and electronic descriptors are critical for achieving reliable predictions. This is the first attempt to combine ML from fragment-based DFT calculations to predict experimental chemical shifts accurately, making the MIM-ML model a valuable tool for NMR predictions of nucleic acids.

Atomic-level structure determination of amorphous molecular solids by NMR

Structure determination of amorphous materials remains challenging, owing to the disorder inherent to these materials. Nuclear magnetic resonance (NMR) powder crystallography is a powerful method to determine the structure of molecular solids, but disorder leads to a high degree of overlap between measured signals, and prevents the unambiguous identification of a single modeled periodic structure as representative of the whole material. Here, we determine the atomic-level ensemble structure of the amorphous form of the drug AZD4625 by combining solid-state NMR experiments with molecular dynamics (MD) simulations and machine-learned chemical shifts. By considering the combined shifts of all 1H and 13C atomic sites in the molecule, we determine the structure of the amorphous form by identifying an ensemble of local molecular environments that are in agreement with experiment. We then extract and analyze preferred conformations and intermolecular interactions in the amorphous sample in terms of the stabilization of the amorphous form of the drug.

Expression and purification of 15N-labeled Fra a 1, a strawberry allergen, to prepare samples for NMR measurements

Raw strawberries contain allergens that cause oral allergic syndrome. Fra a 1 is one of the major allergens in strawberries and might decrease their allergenicity by heating, likely due to structural changes in the allergen leading to decreased recognition of the allergens in the oral cavity. In the present study, to understand the relationship between allergen structure and allergenicity, the expression and purification of 15N-labeled Fra a 1 were examined and the sample was used for NMR analysis. Two isoforms, Fra a 1.01 and Fra a 1.02, were used and expressed in E. coli BL21(DE3) in M9 minimal medium. Fra a 1.02 was purified as a single protein by using the GST tag approach, whereas histidine×6-tag (his6-tag) Fra a 1.02 was obtained both as the full-length (∼20 kDa) and a truncated (∼18 kDa) form. On the other hand, his6-tag Fra a 1.01 was purified as a homogeneous protein. ¹⁵N-labeled HSQC NMR spectra suggested that Fra a 1.02 was thermally denatured at lower temperatures than Fra a 1.01, despite the high amino acid sequence homology (79.4%) of these isoforms. Furthermore, the samples in the present study allowed us to analyze ligand binding that probably affects structural stability. In conclusion, GST tag was effective for obtaining a homogeneous protein when his6-tag failed to give a single form, and the present study provided a sample that could be used for NMR studies of the details of the allergenicity and structure of Fra a 1.

Learning to evolve structural ensembles of unfolded and disordered proteins using experimental solution data

The structural characterization of proteins with a disorder requires a computational approach backed by experiments to model their diverse and dynamic structural ensembles. The selection of conformational ensembles consistent with solution experiments of disordered proteins highly depends on the initial pool of conformers, with currently available tools limited by conformational sampling. We have developed a Generative Recurrent Neural Network (GRNN) that uses supervised learning to bias the probability distributions of torsions to take advantage of experimental data types such as nuclear magnetic resonance J-couplings, nuclear Overhauser effects, and paramagnetic resonance enhancements. We show that updating the generative model parameters according to the reward feedback on the basis of the agreement between experimental data and probabilistic selection of torsions from learned distributions provides an alternative to existing approaches that simply reweight conformers of a static structural pool for disordered proteins. Instead, the biased GRNN, DynamICE, learns to physically change the conformations of the underlying pool of the disordered protein to those that better agree with experiments.

Accurate prediction of 11B NMR chemical shift of BODIPYs via machine learning

In this article, we present the results of developing a model based on an RFR machine learning method using the ISIDA fragment descriptors for predicting the ¹¹B NMR chemical shift of BODIPYs. The model is freely available at https://ochem.eu/article/146458. The model demonstrates the high quality of predicting the ¹¹B NMR chemical shift (RMSE, 5CV (FINALE training set) = 0.40 ppm, RMSE (TEST set) = 0.14 ppm). In addition, we compared the "cost" and the user-friendliness for calculations using the quantum-chemical model with the DFT/GIAO approach. The ¹¹B NMR chemical shift prediction accuracy (RMSE) of the model considered is more than three times higher and tremendously faster than the DFT/GIAO calculations. As a result, we provide a convenient tool and database that we collected for all researchers, that allows them to predict the ¹¹B NMR chemical shift of boron-containing dyes. We believe that the new model will make it easier for researchers to correctly interpret the ¹¹B NMR chemical shifts experimentally determined and to select more optimal conditions to perform an NMR experiment.

Enhancing Biomolecular Simulations with Hybrid Potentials Incorporating NMR Data

Some recent advances in biomolecular simulation and global optimization have used hybrid restraint potentials, where harmonic restraints that penalize conformations inconsistent with experimental data are combined with molecular mechanics force fields. These hybrid potentials can be used to improve the performance of molecular dynamics, structure prediction, energy landscape sampling, and other computational methods that rely on the accuracy of the underlying force field. Here, we develop a hybrid restraint potential based on NapShift, an artificial neural network trained to predict protein nuclear magnetic resonance (NMR) chemical shifts from sequence and structure. In addition to providing accurate predictions of experimental chemical shifts, NapShift is fully differentiable with respect to atomic coordinates, which allows us to use it for structural refinement. By employing NapShift to predict chemical shifts from the protein conformation at each simulation step, we can compute an energy penalty and the corresponding hybrid restraint forces based on the difference between the predicted values and the experimental chemical shifts. The performance of the hybrid restraint potential was benchmarked using both basin-hopping global optimization and molecular dynamics simulations. In each case, the NapShift hybrid potential improved the accuracy, leading to better structure prediction via basin-hopping and increased local stability in molecular dynamics simulations. Our results suggest that neural network hybrid potentials based on NMR observables can enhance a broad range of molecular simulation methods, and the prediction accuracy will improve as more experimental training data become available.

Biological Magnetic Resonance Data Bank

The Biological Magnetic Resonance Data Bank (BMRB, https://bmrb.io) is the international open data repository for biomolecular nuclear magnetic resonance (NMR) data. Comprised of both empirical and derived data, BMRB has applications in the study of biomacromolecular structure and dynamics, biomolecular interactions, drug discovery, intrinsically disordered proteins, natural products, biomarkers, and metabolomics. Advances including GHz-class NMR instruments, national and trans-national NMR cyberinfrastructure, hybrid structural biology methods and machine learning are driving increases in the amount, type, and applications of NMR data in the biosciences. BMRB is a Core Archive and member of the World-wide Protein Data Bank (wwPDB).

SpecDB: A relational database for archiving biomolecular NMR spectral data

NMR is a valuable experimental tool in the structural biologist's toolkit to elucidate the structures, functions, and motions of biomolecules. The progress of machine learning, particularly in structural biology, reveals the critical importance of large, diverse, and reliable datasets in developing new methods and understanding in structural biology and science more broadly. Biomolecular NMR research groups produce large amounts of data, and there is renewed interest in organizing these data to train new, sophisticated machine learning architectures and to improve biomolecular NMR analysis pipelines. The foundational data type in NMR is the free-induction decay (FID). There are opportunities to build sophisticated machine learning methods to tackle long-standing problems in NMR data processing, resonance assignment, dynamics analysis, and structure determination using NMR FIDs. Our goal in this study is to provide a lightweight, broadly available tool for archiving FID data as it is generated at the spectrometer, and grow a new resource of FID data and associated metadata. This study presents a relational schema for storing and organizing the metadata items that describe an NMR sample and FID data, which we call Spectral Database (SpecDB). SpecDB is implemented in SQLite and includes a Python software library providing a command-line application to create, organize, query, backup, share, and maintain the database. This set of software tools and database schema allow users to store, organize, share, and learn from NMR time domain data. SpecDB is freely available under an open source license at https://github.rpi.edu/RPIBioinformatics/SpecDB.

Regression Machine Learning Models Used to Predict DFT-Computed NMR Parameters of Zeolites

Machine learning approaches can drastically decrease the computational time for the predictions of spectroscopic properties in materials, while preserving the quality of the computational approaches. We studied the performance of kernel-ridge regression (KRR) and gradient boosting regressor (GBR) models trained on the isotropic shielding values, computed with density-functional theory (DFT), in a series of different known zeolites containing out-of-frame metal cations or fluorine anion and organic structure-directing cations. The smooth overlap of atomic position descriptors were computed from the DFT-optimised Cartesian coordinates of each atoms in the zeolite crystal cells. The use of these descriptors as inputs in both machine learning regression methods led to the prediction of the DFT isotropic shielding values with mean errors within 0.6 ppm. The results showed that the GBR model scales better than the KRR model.

Aggregation-Prone Structural Ensembles of Transthyretin Collected With Regression Analysis for NMR Chemical Shift

Monomer dissociation and subsequent misfolding of the transthyretin (TTR) is one of the most critical causative factors of TTR amyloidosis. TTR amyloidosis causes several human diseases, such as senile systemic amyloidosis and familial amyloid cardiomyopathy/polyneuropathy; therefore, it is important to understand the molecular details of the structural deformation and aggregation mechanisms of TTR. However, such molecular characteristics are still elusive because of the complicated structural heterogeneity of TTR and its highly sensitive nature to various environmental factors. Several nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) studies of TTR variants have recently reported evidence of transient aggregation-prone structural states of TTR. According to these studies, the stability of the DAGH β-sheet, one of the two main β-sheets in TTR, is a crucial determinant of the TTR amyloidosis mechanism. In addition, its conformational perturbation and possible involvement of nearby structural motifs facilitates TTR aggregation. This study proposes aggregation-prone structural ensembles of TTR obtained by MD simulation with enhanced sampling and a multiple linear regression approach. This method provides plausible structural models that are composed of ensemble structures consistent with NMR chemical shift data. This study validated the ensemble models with experimental data obtained from circular dichroism (CD) spectroscopy and NMR order parameter analysis. In addition, our results suggest that the structural deformation of the DAGH β-sheet and the AB loop regions may correlate with the manifestation of the aggregation-prone conformational states of TTR. In summary, our method employing MD techniques to extend the structural ensembles from NMR experimental data analysis may provide new opportunities to investigate various transient yet important structural states of amyloidogenic proteins.

Protein C-GeM: A Coarse-Grained Electron Model for Fast and Accurate Protein Electrostatics Prediction

The electrostatic potential (ESP) is a powerful property for understanding and predicting electrostatic charge distributions that drive interactions between molecules. In this study, we compare various charge partitioning schemes including fitted charges, density-based quantum mechanical (QM) partitioning schemes, charge equilibration methods, and our recently introduced coarse-grained electron model, C-GeM, to describe the ESP for protein systems. When benchmarked against high quality density functional theory calculations of the ESP for tripeptides and the crambin protein, we find that the C-GeM model is of comparable accuracy to ab initio charge partitioning methods, but with orders of magnitude improvement in computational efficiency since it does not require either the electron density or the electrostatic potential as input.

Ab Initio Machine Learning in Chemical Compound Space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.

On the potential of machine learning to examine the relationship between sequence, structure, dynamics and function of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as having no persistent tertiary structure; instead they interconvert between a large number of different and often expanded structures. IDPs and IDRs are involved in an enormously wide range of biological functions and reveal novel mechanisms of interactions, and while they defy the common structure-function paradigm of folded proteins, their structural preferences and dynamics are important for their function. We here discuss open questions in the field of IDPs and IDRs, focusing on areas where machine learning and other computational methods play a role. We discuss computational methods aimed to predict transiently formed local and long-range structure, including methods for integrative structural biology. We discuss the many different ways in which IDPs and IDRs can bind to other molecules, both via short linear motifs, as well as in the formation of larger dynamic complexes such as biomolecular condensates. We discuss how experiments are providing insight into such complexes and may enable more accurate predictions. Finally, we discuss the role of IDPs in disease and how new methods are needed to interpret the mechanistic effects of genomic variants in IDPs.

Accurate Structure Prediction for Protein Loops Based on Molecular Dynamics Simulations with RSFF2C

Protein loops, connecting the α-helices and β-strands, are involved in many important biological processes. However, due to their conformational flexibility, it is still challenging to accurately determine three-dimensional (3D) structures of long loops experimentally and computationally. Herein, we present a systematic study of the protein loop structure prediction via a total of ∼850 μs molecular dynamics (MD) simulations. For a set of 15 long (10-16 residues) and solvent-exposed loops, we first evaluated the performance of four state-of-the-art loop modeling algorithms, DaReUS-Loop, Sphinx, Rosetta-NGK, and MODELLER, on each loop, and none of them could accurately predict the structures for most loops. Then, temperature replica exchange molecular dynamics (REMD) simulations were conducted with three recent force fields, RSFF2C with TIP3P water model, CHARMM36m with CHARMM-modified TIP3P, and AMBER ff19SB with OPC. We found that our recently developed residue-specific force field RSFF2C performed the best and successfully predicted 12 out of 15 loops with a root-mean-square deviation (RMSD) < 1.5 Å. As an alternative with lower computational cost, normal MD simulations at high temperatures (380, 500, and 620 K) were investigated. Temperature-dependent performance was observed for each force field, and, for RSFF2C+TIP3P, we found that three independent 100-ns MD simulations at 500 K gave comparable results with REMD simulations. These results suggest that MD simulations, especially with enhanced sampling techniques such as replica exchange, with the RSFF2C force field could be useful for accurate loop structure prediction.

Improved Prediction of Carbonless NMR Spectra by the Machine Learning of Theoretical and Fragment Descriptors for Environmental Mixture Analysis

As the first multidimensional NMR approach, 2D J-resolved (2DJ) spectroscopy is distinguished by signal resolution and detection sensitivity with remarkable advantages for the exhaustive evaluation of complex mixtures and environmental samples due to its carbonless feature without the requirement of ¹³C connectivity. Generally, the 2DJ signal assignment of metabolic mixtures is problematic in spite of references to experimental NMR databases, owing to the existence of metabolic "dark matter." In this study, a new method to predict 2DJ spectra was developed with a combination of quantum mechanical (QM) computation and machine learning (ML). The predictive accuracy of J-coupling constants was evaluated using validated data. The root-mean-square deviation (RMSD) for QM computation was 3.52 Hz, while the RMSD for QM + ML was 1.21 Hz, indicating a substantial increase in predictive accuracy. The proposed model was applied to predict the 2DJ spectra of 60 standard substances and 55 components of seawater. Furthermore, two practical environmental samples were used to evaluate the robustness of the constructed predictive model. A J-coupling tree and J-split spectra produced from QM + ML of aliphatic moieties had good consistency with the experimental data, as compared with the theoretical data produced by QM computation. The predicted J-coupling tree for the J-coupling multiplet analysis of freely rotating bonds in the complex mixture, which is traditionally difficult, was interpretable. In addition, in silico identification of the J-split ¹H NMR signals, which was independent of experimental databases, aided in the discovery of new components in a mixture.

Exploiting Machine Learning to Efficiently Predict Multidimensional Optical Spectra in Complex Environments

The excited-state dynamics of chromophores in complex environments determine a range of vital biological and energy capture processes. Time-resolved, multidimensional optical spectroscopies provide a key tool to investigate these processes. Although theory has the potential to decode these spectra in terms of the electronic and atomistic dynamics, the need for large numbers of excited-state electronic structure calculations severely limits first-principles predictions of multidimensional optical spectra for chromophores in the condensed phase. Here, we leverage the locality of chromophore excitations to develop machine learning models to predict the excited-state energy gap of chromophores in complex environments for efficiently constructing linear and multidimensional optical spectra. By analyzing the performance of these models, which span a hierarchy of physical approximations, across a range of chromophore-environment interaction strengths, we provide strategies for the construction of machine learning models that greatly accelerate the calculation of multidimensional optical spectra from first principles.

Extended Experimental Inferential Structure Determination Method in Determining the Structural Ensembles of Disordered Protein States

Proteins with intrinsic or unfolded state disorder comprise a new frontier in structural biology, requiring the characterization of diverse and dynamic structural ensembles. We introduce a comprehensive Bayesian framework, the Extended Experimental Inferential Structure Determination (X-EISD) method, that calculates the maximum log-likelihood of a disordered protein ensemble. X-EISD accounts for the uncertainties of a range of experimental data and back-calculation models from structures, including NMR chemical shifts, J-couplings, Nuclear Overhauser Effects (NOEs), paramagnetic relaxation enhancements (PREs), residual dipolar couplings (RDCs), hydrodynamic radii (R _h ), single molecule fluorescence Förster resonance energy transfer (smFRET) and small angle X-ray scattering (SAXS). We apply X-EISD to the joint optimization against experimental data for the unfolded drkN SH3 domain and find that combining a local data type, such as chemical shifts or J-couplings, paired with long-ranged restraints such as NOEs, PREs or smFRET, yields structural ensembles in good agreement with all other data types if combined with representative IDP conformers.