Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Solid-state NMR chemical shift analysis for determining the conformation of ATP bound to Na,K-ATPase in its native membrane

Structures of membrane proteins determined by X-ray crystallography and, increasingly, by cryo-electron microscopy often fail to resolve the structural details of unstable or reactive small molecular ligands in their physiological sites. This work demonstrates that 13C chemical shifts measured by magic-angle spinning (MAS) solid-state NMR (SSNMR) provide unique information on the conformation of a labile ligand in the physiological site of a functional protein in its native membrane, by exploiting freeze-trapping to stabilise the complex. We examine the ribose conformation of ATP in a high affinity complex with Na,K-ATPase (NKA), an enzyme that rapidly hydrolyses ATP to ADP and inorganic phosphate under physiological conditions. The 13C SSNMR spectrum of the frozen complex exhibits peaks from all ATP ribose carbon sites and some adenine base carbons. Comparison of experimental chemical shifts with density functional theory (DFT) calculations of ATP in different conformations and protein environments reveals that the ATP ribose ring adopts an C3'-endo (N) conformation when bound with high affinity to NKA in the E1Na state, in contrast to the C2'-endo (S) ribose conformations of ATP bound to the E2P state and AMPPCP in the E1 complex. Additional dipolar coupling-mediated measurements of H-C-C-H torsional angles are used to eliminate possible relative orientations of the ribose and adenine rings. The utilization of chemical shifts to determine membrane protein ligand conformations has been underexploited to date and here we demonstrate this approach to be a powerful tool for resolving the fine details of ligand-protein interactions.

Benchmark accuracy of predicted NMR observables for quadrupolar 14 N and 17 O nuclei in molecular crystals

Nuclear quadrupole resonances for 14 N and ¹⁷ O nuclei are exquisitely sensitive to interactions with surrounding atoms. As a result, nitrogen and oxygen solid-state nuclear magnetic resonance (ssNMR) provides a powerful tool for investigating structure and dynamics in complex systems. First-principles calculations are increasingly used to facilitate spectral assignment and to evaluate and adjust crystal structures. Recent work combining the strengths of planewave density functional theory (DFT) calculations with a single molecule correction obtained using a higher level of theory has proven successful in improving the accuracy of predicted chemical shielding (CS) tensors and ¹⁷ O quadrupolar coupling constants ( C q ). Here we extend this work by examining the accuracy of predicted ¹⁴ N and ¹⁷ O electric field gradient (EFG) tensor components obtained using alternative planewave-corrections involving cluster and two-body fragment-based calculations. We benchmark the accuracy of CS and EFG tensor predictions for both nitrogen and oxygen using planewave, two-body fragment, and enhanced planewave-corrected techniques. Combining planewave and two-body fragment calculations reduces the error in predicted ¹⁷ O C q values by 35% relative to traditional planewave calculations. These enhanced planewave-correction methods improve the accuracy of ¹⁷ O and ¹⁴ N EFG tensor components by 15% relative to planewave DFT but yield minimal improvement relative to a simple molecular correction. However, in structural environments involving either high symmetry or strong intermolecular interactions, enhanced planewave-corrected methods provide a distinct advantage.

Improving the accuracy of GIPAW chemical shielding calculations with cluster and fragment corrections

Ab initio methods for predicting NMR parameters in the solid state are an essential tool for assigning experimental spectra and play an increasingly important role in structural characterizations. Recently, a molecular correction (MC) technique has been developed which combines the strengths of plane-wave methods (GIPAW) with single molecule calculations employing Gaussian basis sets. The GIPAW + MC method relies on a periodic calculation performed at a lower level of theory to model the crystalline environment. The GIPAW result is then corrected using a single molecule calculation performed at a higher level of theory. The success of the GIPAW + MC method in predicting a range of NMR parameters is a result of the highly local character of the tensors underlying the NMR observable. However, in applications involving strong intermolecular interactions we find that expanding the region treated at the higher level of theory more accurately captures local many-body contributions to the N15 NMR chemical shielding (CS) tensor. We propose alternative corrections to GIPAW which capture interactions between adjacent molecules at a higher level of theory using either fragment or cluster-based calculations. Benchmark calculations performed on N15 and C13 data sets show that these advanced GIPAW-corrected calculations improve the accuracy of chemical shielding tensor predictions relative to existing methods. Specifically, cluster-based N15 corrections show a 24% and 17% reduction in RMS error relative to GIPAW and GIPAW + MC calculations, respectively. Comparing the benchmark data sets using multiple computational models demonstrates that N15 CS tensor calculations are significantly more sensitive to intermolecular interactions relative to C13. However, fragment and cluster-based corrections that include direct hydrogen bond partners are sufficient for optimizing the accuracy of GIPAW-corrected methods. Finally, GIPAW-corrected methods are applied to the particularly challenging NMR spectral assignment of guanosine dihydrate which contains two guanosine molecules in the asymmetric unit.

Convergence in determining enzyme functional descriptors across Kemp eliminase variants

Molecular simulations have been extensively employed to accelerate biocatalytic discoveries. Enzyme functional descriptors derived from molecular simulations have been leveraged to guide the search for beneficial enzyme mutants. However, the ideal active-site region size for computing the descriptors over multiple enzyme variants remains untested. Here, we conducted convergence tests for dynamics-derived and electrostatic descriptors on 18 Kemp eliminase variants across six active-site regions with various boundary distances to the substrate. The tested descriptors include the root-mean-square deviation of the active-site region, the solvent accessible surface area ratio between the substrate and active site, and the projection of the electric field (EF) on the breaking C-H bond. All descriptors were evaluated using molecular mechanics methods. To understand the effects of electronic structure, the EF was also evaluated using quantum mechanics/molecular mechanics methods. The descriptor values were computed for 18 Kemp eliminase variants. Spearman correlation matrices were used to determine the region size condition under which further expansion of the region boundary does not substantially change the ranking of descriptor values. We observed that protein dynamics-derived descriptors, including RMSD_{active_site} and SASA_ratio, converge at a distance cutoff of 5 Å from the substrate. The electrostatic descriptor, EF_C-H, converges at 6 Å using molecular mechanics methods with truncated enzyme models and 4 Å using quantum mechanics/molecular mechanics methods with whole enzyme model. This study serves as a future reference to determine descriptors for predictive modeling of enzyme engineering.

Factors That Determine the Variation of Equilibrium and Kinetic Properties of QM/MM Enzyme Simulations: QM Region, Conformation, and Boundary Condition

To analyze the impact of various technical details on the results of quantum mechanical (QM)/molecular mechanical (MM) enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ∼100 to ∼500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

Atomic-resolution chemical characterization of (2x)72-kDa tryptophan synthase via four- and five-dimensional 1H-detected solid-state NMR

NMR chemical shifts provide detailed information on the chemical properties of molecules, thereby complementing structural data from techniques like X-ray crystallography and electron microscopy. Detailed analysis of protein NMR data, however, often hinges on comprehensive, site-specific assignment of backbone resonances, which becomes a bottleneck for molecular weights beyond 40 to 45 kDa. Here, we show that assignments for the (2x)72-kDa protein tryptophan synthase (665 amino acids per asymmetric unit) can be achieved via higher-dimensional, proton-detected, solid-state NMR using a single, 1-mg, uniformly labeled, microcrystalline sample. This framework grants access to atom-specific characterization of chemical properties and relaxation for the backbone and side chains, including those residues important for the catalytic turnover. Combined with first-principles calculations, the chemical shifts in the β-subunit active site suggest a connection between active-site chemistry, the electrostatic environment, and catalytically important dynamics of the portal to the β-subunit from solution.

Imaging active site chemistry and protonation states: NMR crystallography of the tryptophan synthase α-aminoacrylate intermediate

NMR-assisted crystallography-the integrated application of solid-state NMR, X-ray crystallography, and first-principles computational chemistry-holds significant promise for mechanistic enzymology: by providing atomic-resolution characterization of stable intermediates in enzyme active sites, including hydrogen atom locations and tautomeric equilibria, NMR crystallography offers insight into both structure and chemical dynamics. Here, this integrated approach is used to characterize the tryptophan synthase α-aminoacrylate intermediate, a defining species for pyridoxal-5'-phosphate-dependent enzymes that catalyze β-elimination and replacement reactions. For this intermediate, NMR-assisted crystallography is able to identify the protonation states of the ionizable sites on the cofactor, substrate, and catalytic side chains as well as the location and orientation of crystallographic waters within the active site. Most notable is the water molecule immediately adjacent to the substrate β-carbon, which serves as a hydrogen bond donor to the ε-amino group of the acid-base catalytic residue βLys87. From this analysis, a detailed three-dimensional picture of structure and reactivity emerges, highlighting the fate of the L-serine hydroxyl leaving group and the reaction pathway back to the preceding transition state. Reaction of the α-aminoacrylate intermediate with benzimidazole, an isostere of the natural substrate indole, shows benzimidazole bound in the active site and poised for, but unable to initiate, the subsequent bond formation step. When modeled into the benzimidazole position, indole is positioned with C3 in contact with the α-aminoacrylate Cβ and aligned for nucleophilic attack. Here, the chemically detailed, three-dimensional structure from NMR-assisted crystallography is key to understanding why benzimidazole does not react, while indole does.

Mutation of βGln114 to Ala Alters the Stabilities of Allosteric States in Tryptophan Synthase Catalysis

The tryptophan synthase (TS) bienzyme complexes found in bacteria, yeasts, and molds are pyridoxal 5'-phosphate (PLP)-requiring enzymes that synthesize l-Trp. In the TS catalytic cycle, switching between the open and closed states of the α- and β-subunits via allosteric interactions is key to the efficient conversion of 3-indole-d-glycerol-3'-phosphate and l-Ser to l-Trp. In this process, the roles played by β-site residues proximal to the PLP cofactor have not yet been fully established. βGln114 is one such residue. To explore the roles played by βQ114, we conducted a detailed investigation of the βQ114A mutation on the structure and function of tryptophan synthase. Initial steady-state kinetic and static ultraviolet-visible spectroscopic analyses showed the Q to A mutation impairs catalytic activity and alters the stabilities of intermediates in the β-reaction. Therefore, we conducted X-ray structural and solid-state nuclear magnetic resonance spectroscopic studies to compare the wild-type and βQ114A mutant enzymes. These comparisons establish that the protein structural changes are limited to the Gln to Ala replacement, the loss of hydrogen bonds among the side chains of βGln114, βAsn145, and βArg148, and the inclusion of waters in the cavity created by substitution of the smaller Ala side chain. Because the conformations of the open and closed allosteric states are not changed by the mutation, we hypothesize that the altered properties arise from the lost hydrogen bonds that alter the relative stabilities of the open (β^T state) and closed (β^R state) conformations of the β-subunit and consequently alter the distribution of intermediates along the β-subunit catalytic path.

Harder, better, faster, stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Tradeoffs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multiscale QM/MM or iterative approach. Limitations to both conventional density-functional theory and classical MM force fields remain for describing noncovalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e. electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.

Accurate fragment-based 51-V chemical shift predictions in molecular crystals

Nuclear magnetic resonance (NMR) spectroscopy plays a crucial role in determining molecular structure for complex biological and pharmaceutical compounds. NMR investigations are increasingly reliant on computation for mapping spectral features to chemical structures. Here we benchmark the accuracy of fragment-based ⁵¹V chemical shielding tensor calculations using a training set comprised of 10 biologically and pharmaceutically relevant oxovanadium complexes. Using our self-consistent reproduction of the Madelung potential (SCRMP) electrostatic embedding model, we demonstrate comparable performance between fragment methods and computationally demanding cluster-based techniques. Specifically, fragment methods employing hybrid density functionals are capable of reproducing the experimental ⁵¹V isotropic chemical shifts with a training set rms error of ~9 ​ppm, representing a 20% improvement over traditional plane wave techniques. We provide training set-derived linear regression models for mapping the absolute shieldings obtained from computation to the experimentally determined chemical shifts using four common density functionals; PBE0, B3LYP, PBE, and BLYP. Finally, we establish the utility of fragment methods and the reported regression parameters examining four oxovanadium structures excluded from the training set including the tetracoordinate oxovanadium silicate [Formula: see text] , VO¹⁵NGlySalbz which contains redox-active ligands, and the solid-state form of the common ⁵¹V NMR reference compound VOCl₃.

Combining Evolutionary Conservation and Quantum Topological Analyses To Determine Quantum Mechanics Subsystems for Biomolecular Quantum Mechanics/Molecular Mechanics Simulations

Selection of residues and other molecular fragments for inclusion in the quantum mechanics (QM) region for QM/molecular mechanics (MM) simulations is an important step for these calculations. Here, we present an approach that combines protein sequence/structure evolution and electron localization function (ELF) analyses. The combination of these two analyses allows the determination of whether a residue needs to be included in the QM subsystem or can be represented by the MM environment. We have applied this approach on two systems previously investigated by QM/MM simulations, 4-oxalocrotonate tautomerase (4OT) and ten-eleven translocation-2 (TET2), that provide examples where fragments may or may not need to be included in the QM subsystem. Subsequently, we present the use of this approach to determine the appropriate QM subsystem to calculate the minimum energy path (MEP) for the reaction catalyzed by human DNA polymerase λ (Polλ) with a third cation in the active site. Our results suggest that the combination of protein evolutionary and ELF analyses provides insights into residue/molecular fragment selection for QM/MM simulations.

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

Predicting 19 F NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase-Inhibitor Complex

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor-protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable 19 F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the 19 F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein-inhibitor conformations as well as monomeric and dimeric inhibitor-protein complexes, thus rendering it the largest computational study on chemical shifts of 19 F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.

Both Configuration and QM Region Size Matter: Zinc Stability in QM/MM Models of DNA Methyltransferase

Quantum-mechanical/molecular-mechanical (QM/MM) methods are essential to the study of metalloproteins, but the relative importance of sampling and degree of QM treatment in achieving quantitative predictions is poorly understood. We study the relative magnitude of configurational and QM-region sensitivity of energetic and electronic properties in a representative Zn²⁺ metal binding site of a DNA methyltransferase. To quantify property variations, we analyze snapshots extracted from 250 ns of molecular dynamics simulation. To understand the degree of QM-region sensitivity, we perform analysis using QM regions ranging from a minimal 49-atom region consisting only of the Zn²⁺ metal and its four coordinating Cys residues up to a 628-atom QM region that includes residues within 12 Å of the metal center. Over the configurations sampled, we observe that illustrative properties (e.g., rigid Zn²⁺ removal energy) exhibit large fluctuations that are well captured with even minimal QM regions. Nevertheless, for both energetic and electronic properties, we observe a slow approach to asymptotic limits with similarly large changes in absolute values that converge only with larger (ca. 300-atom) QM region sizes. For the smaller QM regions, the electronic description of Zn²⁺ binding is incomplete: the metal binds too tightly and is too stabilized by the strong electrostatic potential of MM point charges, and the Zn-S bond covalency is overestimated. Overall, this work suggests that efficient sampling with QM/MM in small QM regions is an effective method to explore the influence of enzyme structure on target properties. At the same time, accurate descriptions of electronic and energetic properties require a larger QM region than the minimal metal-coordinating residues in order to converge treatment of both metal-local bonding and the overall electrostatic environment.

Improving Predicted Nuclear Magnetic Resonance Chemical Shifts Using the Quasi-Harmonic Approximation

Ab initio nuclear magnetic resonance chemical shift prediction plays an important role in the determination or validation of crystal structures. The ability to predict chemical shifts more accurately can translate to increased confidence in the resulting chemical shift or structural assignments. Standard electronic structure predictions for molecular crystal structures neglect thermal expansion, which can lead to an appreciable underestimation of the molar volumes. This study examines this volume error and its impact on 68 ¹³C- and 28 ¹⁵N-predicted chemical shifts taken from 20 molecular crystals. It assesses the ability to recover more realistic room-temperature crystal structures using the quasi-harmonic approximation and how refining the structures impacts the chemical shifts. Several pharmaceutical molecular crystals are also examined in more detail. On the whole, accounting for quasi-harmonic expansion changes the ¹³C and ¹⁵N chemical shifts by 0.5 and 1.0 ppm on average. This, in turn, reduces the root-mean-square errors relative to experiment by 0.3 ppm for ¹³C and 0.7 ppm for ¹⁵N. Although the statistical impacts are modest, changes in individual chemical shifts can reach multiple ppm. Accounting for thermal expansion in molecular crystal chemical shift prediction may not be needed routinely, but the systematic trend toward improved accuracy with the experiment could be useful in cases where discrimination between structural candidates is challenging, as in the pharmaceutical theophylline.

A benchmark for the size of the QM system required for accurate hybrid QM/MM calculations on the metal site of the protein copper, zinc superoxide dismutase

The protein superoxide dismutase 1 (SOD1) is a copper and zinc-binding protein that has been implicated in the pathogenesis of amyotrophic lateral sclerosis (ALS). The Zn(II) binding to SOD1 is critical for the stability of the protein, and has been by itself implicated in ALS pathogenesis. Hence, the quantum mechanical (QM) study of the Zn(II)-site of SOD1 is relevant for understanding ALS. The hybrid QM-molecular mechanics (QM/MM) approach commonly employed for the QM study of proteins is highly dependent on the size of the sub-system treated quantum-mechanically. The size of the QM system also determines the computational feasibility of a given method. In the present work, we compare optimized geometries for the metal site and Zn(II) dissociation energies obtained with a QM/MM methodology employing different sizes for the QM sub-system. We find that geometries converge rapidly to RMSDs of around 0.3 Å, and fails to converge further, while a QM system of 480 atoms was required for converging the Zn(II) interaction energy of SOD1 to within 5 kcal*mol^-1, and a 611-atoms QM system for a 1 kcal*mol^-1 convergence with respect to our reference, 1280 QM-atoms system. Graphical Abstract The size of the QM system is critical for both the accuracy and the computational cost of a QM/MM calculation. We have identified a optimum balance for the study of the active site of the coppper, zinc superoxide dismutase.

TensorView: A software tool for displaying NMR tensors

The representation of nuclear magnetic resonance (NMR) tensors as surfaces on three-dimensional molecular models is an information-rich presentation that highlights the geometric relationship between tensor principal components and the underlying molecular and electronic structure. Here, we describe a new computational tool, TensorView, for depicting NMR tensors on the molecular framework. This package makes use of the graphical interface and built-in molecular display functionality present within the Mathematica programming environment and is robust for displaying tensor properties from a broad range of commercial and user-specific computational chemistry packages. Two mathematical forms for representing tensor interaction surfaces are presented, the popular ellipsoidal construct and the more technically correct "ovaloid" form. Examples are provided for chemical shielding and shift tensors, dipole-dipole and quadrupolar couplings, and atomic anisotropic displacement parameters (thermal ellipsoids) derived from NMR crystallography.

Revealing quantum mechanical effects in enzyme catalysis with large-scale electronic structure simulation

Enzymes have evolved to facilitate challenging reactions at ambient conditions with specificity seldom matched by other catalysts. Computational modeling provides valuable insight into catalytic mechanism, and the large size of enzymes mandates multi-scale, quantum mechanical-molecular mechanical (QM/MM) simulations. Although QM/MM plays an essential role in balancing simulation cost to enable sampling with full QM treatment needed to understand electronic structure in enzyme active sites, the relative importance of these two strategies for understanding enzyme mechanism is not well known. We explore challenges in QM/MM for studying the reactivity and stability of three diverse enzymes: i) Mg2+-dependent catechol O-methyltransferase (COMT), ii) radical enzyme choline trimethylamine lyase (CutC), and iii) DNA methyltransferase (DNMT1), which has structural Zn2+ binding sites. In COMT, strong non-covalent interactions lead to long range coupling of electronic structure properties across the active site, but the more isolated nature of the metallocofactor in DNMT1 leads to faster convergence of some properties. We quantify these effects in COMT by computing covariance matrices of by-residue electronic structure properties during dynamics and along the reaction coordinate. In CutC, we observe spontaneous bond cleavage following initiation events, highlighting the importance of sampling and dynamics. We use electronic structure analysis to quantify the relative importance of CHO and OHO non-covalent interactions in imparting reactivity. These three diverse cases enable us to provide some general recommendations regarding QM/MM simulation of enzymes.

Computational Understanding of the Selectivities in Metalloenzymes

Metalloenzymes catalyze many different types of biological reactions with high efficiency and remarkable selectivity. The quantum chemical cluster approach and the combined quantum mechanics/molecular mechanics methods have proven very successful in the elucidation of the reaction mechanism and rationalization of selectivities in enzymes. In this review, recent progress in the computational understanding of various selectivities including chemoselectivity, regioselectivity, and stereoselectivity, in metalloenzymes, is discussed.

Accurate 13-C and 15-N molecular crystal chemical shielding tensors from fragment-based electronic structure theory

Standard nuclear magnetic resonance (NMR) spectroscopy experiments measure isotropic chemical shifts, but measuring the chemical shielding anisotropy (CSA) tensor can provide additional insights into solid state chemical structures. Interpreting the principal components of these tensors is facilitated by first-principles chemical shielding tensor predictions. Here, the ability to predict molecular crystal CSA tensor components for ¹³C and ¹⁵N nuclei with fragment-based electronic structure techniques is explored. Similar to what has been found previously for isotropic chemical shifts, the benchmarking demonstrates that fragment-based techniques can accurately reproduce CSA tensor components. The use of hybrid density functionals like PBE0 or B3LYP provide higher accuracy than generalized gradient approximation functionals like PBE. Unlike for planewave density functional techniques, hybrid density functionals can be employed routinely with modest computational cost in fragment approaches. Finally, good consistency between the regression parameters used to map either isotropic shieldings or CSA tensor components is demonstrated, providing further evidence for the quality of the models and highlighting that models trained for isotropic shifts can also be applied to CSA tensor components.

Do Better Quality Embedding Potentials Accelerate the Convergence of QM/MM Models? The Case of Solvated Acid Clusters

This study examines whether the use of more accurate embedding potentials improves the convergence of quantum mechanics/molecular mechanics (QM/MM) models with respect to the size of the QM region. In conjunction with density functional theory calculations using the ωB97X-D functional, various embedding potentials including the TIP3P water model, the effective fragment potential (EFP), and semi-empirical methods (PM6, PM7, and DFTB) were used to simulate the deprotonation energies of solvated acid clusters. The calculations were performed on solvated neutral (HA) and cationic (HB⁺) acids clusters containing 160 and 480 water molecules using configurations sampled from molecular dynamics simulations. Consistently, the ωB97X-D/EFP model performed the best when using a minimal QM region size. The performance for the other potentials appears to be highly sensitive to the charge character of the acid/base pair. Neutral acids display the expected trend that semi-empirical methods generally perform better than TIP3P; however, an opposite trend was observed for the cationic acids. Additionally, electronic embedding provided an improvement over mechanical embedding for the cationic systems, but not the neutral acids. For the best performing ωB97X-D/EFP model, a QM region containing about 6% of the total number of solvent molecules is needed to approach within 10 kJ mol^-1 of the pure QM result if the QM region was chosen based on the distance from the reaction centre.

Large-scale QM/MM free energy simulations of enzyme catalysis reveal the influence of charge transfer

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations provide key insights into enzyme structure-function relationships. Numerous studies have demonstrated that large QM regions are needed to systematically converge ground state, zero temperature properties with electrostatic embedding QM/MM. However, it is not well known if ab initio QM/MM free energy simulations have this same dependence, in part due to the hundreds of thousands of energy evaluations required for free energy estimations that in turn limit QM region size. Here, we leverage recent advances in electronic structure efficiency and accuracy to carry out range-separated hybrid density functional theory free energy simulations in a representative methyltransferase. By studying 200 ps of ab initio QM/MM dynamics for each of five QM regions from minimal (64 atoms) to one-sixth of the protein (544 atoms), we identify critical differences between large and small QM region QM/MM in charge transfer between substrates and active site residues as well as in geometric structure and dynamics that coincide with differences in predicted free energy barriers. Distinct geometric and electronic structure features in the largest QM region indicate that important aspects of enzymatic rate enhancement in methyltransferases are identified with large-scale electronic structure.

Determination of accurate backbone chemical shift tensors in microcrystalline proteins by integrating MAS NMR and QM/MM

Chemical shifts are highly sensitive probes of local conformation and overall structure. Both isotropic shifts and chemical shift tensors are readily accessible from NMR experiments but their quantum mechanical calculations remain challenging. In this work, we report and compare accurately measured and calculated 15NH and 13Cα chemical shift tensors in proteins, using the microcrystalline agglutinin from Oscillatoria agardhii (OAA). Experimental 13Cα and 15NH chemical tensors were obtained by solid-state NMR spectroscopy, employing tailored recoupling sequences, and for their quantum mechanics/molecular mechanics (QM/MM) calculations different sets of functionals were evaluated. We show that 13Cα chemical shift tensors are primarily determined by backbone dihedral angles and dynamics, while 15NH tensors mainly depend on local electrostatic contributions from solvation and hydrogen bonding. In addition, the influence of including crystallographic waters, the molecular mechanics geometry optimization protocol, and the level of theory on the accuracy of the calculated chemical shift tensors is discussed. Specifically, the power of QM/MM calculations in accurately predicting the unusually upfield shifted 1HN G26 and G93 resonances is highlighted. Our integrated approach is expected to benefit structure refinement of proteins and protein assemblies.

Improved Electrostatic Embedding for Fragment-Based Chemical Shift Calculations in Molecular Crystals

Fragment-based methods predict nuclear magnetic resonance (NMR) chemical shielding tensors in molecular crystals with high accuracy and computational efficiency. Such methods typically employ electrostatic embedding to mimic the crystalline environment, and the quality of the results can be sensitive to the embedding treatment. To improve the quality of this embedding environment for fragment-based molecular crystal property calculations, we borrow ideas from the embedded ion method to incorporate self-consistently polarized Madelung field effects. The self-consistent reproduction of the Madelung potential (SCRMP) model developed here constructs an array of point charges that incorporates self-consistent lattice polarization and which reproduces the Madelung potential at all atomic sites involved in the quantum mechanical region of the system. The performance of fragment- and cluster-based ¹H, ¹³C, ¹⁴N, and ¹⁷O chemical shift predictions using SCRMP and density functionals like PBE and PBE0 are assessed. The improved embedding model results in substantial improvements in the predicted ¹⁷O chemical shifts and modest improvements in the ¹⁵N ones. Finally, the performance of the model is demonstrated by examining the assignment of the two oxygen chemical shifts in the challenging γ-polymorph of glycine. Overall, the SCRMP-embedded NMR chemical shift predictions are on par with or more accurate than those obtained with the widely used gauge-including projector augmented wave (GIPAW) model.

Automated Fragmentation Polarizable Embedding Density Functional Theory (PE-DFT) Calculations of Nuclear Magnetic Resonance (NMR) Shielding Constants of Proteins with Application to Chemical Shift Predictions

Full-protein nuclear magnetic resonance (NMR) shielding constants based on ab initio calculations are desirable, because they can assist in elucidating protein structures from NMR experiments. In this work, we present NMR shielding constants computed using a new automated fragmentation (J. Phys. Chem. B 2009, 113, 10380-10388) approach in the framework of polarizable embedding density functional theory. We extend our previous work to give both basis set recommendations and comment on how large the quantum mechanical region should be to successfully compute ¹³C NMR shielding constants that are comparable with experiment. The introduction of a probabilistic linear regression model allows us to substantially reduce the number of snapshots that are needed to make comparisons with experiment. This approach is further improved by augmenting snapshot selection with chemical shift predictions by which we can obtain a representative subset of snapshots that gives the smallest predicted error, compared to experiment. Finally, we use this subset of snapshots to calculate the NMR shielding constants at the PE-KT3/pcSseg-2 level of theory for all atoms in the protein GB3.

NMR Crystallography of a Carbanionic Intermediate in Tryptophan Synthase: Chemical Structure, Tautomerization, and Reaction Specificity

Carbanionic intermediates play a central role in the catalytic transformations of amino acids performed by pyridoxal-5'-phosphate (PLP)-dependent enzymes. Here, we make use of NMR crystallography-the synergistic combination of solid-state nuclear magnetic resonance, X-ray crystallography, and computational chemistry-to interrogate a carbanionic/quinonoid intermediate analogue in the β-subunit active site of the PLP-requiring enzyme tryptophan synthase. The solid-state NMR chemical shifts of the PLP pyridine ring nitrogen and additional sites, coupled with first-principles computational models, allow a detailed model of protonation states for ionizable groups on the cofactor, substrates, and nearby catalytic residues to be established. Most significantly, we find that a deprotonated pyridine nitrogen on PLP precludes formation of a true quinonoid species and that there is an equilibrium between the phenolic and protonated Schiff base tautomeric forms of this intermediate. Natural bond orbital analysis indicates that the latter builds up negative charge at the substrate Cα and positive charge at C4' of the cofactor, consistent with its role as the catalytic tautomer. These findings support the hypothesis that the specificity for β-elimination/replacement versus transamination is dictated in part by the protonation states of ionizable groups on PLP and the reacting substrates and underscore the essential role that NMR crystallography can play in characterizing both chemical structure and dynamics within functioning enzyme active sites.

Predicting Molecular Crystal Properties from First Principles: Finite-Temperature Thermochemistry to NMR Crystallography

Molecular crystals occur widely in pharmaceuticals, foods, explosives, organic semiconductors, and many other applications. Thanks to substantial progress in electronic structure modeling of molecular crystals, attention is now shifting from basic crystal structure prediction and lattice energy modeling toward the accurate prediction of experimentally observable properties at finite temperatures and pressures. This Account discusses how fragment-based electronic structure methods can be used to model a variety of experimentally relevant molecular crystal properties. First, it describes the coupling of fragment electronic structure models with quasi-harmonic techniques for modeling the thermal expansion of molecular crystals, and what effects this expansion has on thermochemical and mechanical properties. Excellent agreement with experiment is demonstrated for the molar volume, sublimation enthalpy, entropy, and free energy, and the bulk modulus of phase I carbon dioxide when large basis second-order Møller-Plesset perturbation theory (MP2) or coupled cluster theories (CCSD(T)) are used. In addition, physical insight is offered into how neglect of thermal expansion affects these properties. Zero-point vibrational motion leads to an appreciable expansion in the molar volume; in carbon dioxide, it accounts for around 30% of the overall volume expansion between the electronic structure energy minimum and the molar volume at the sublimation point. In addition, because thermal expansion typically weakens the intermolecular interactions, neglecting thermal expansion artificially stabilizes the solid and causes the sublimation enthalpy to be too large at higher temperatures. Thermal expansion also frequently weakens the lower-frequency lattice phonon modes; neglecting thermal expansion causes the entropy of sublimation to be overestimated. Interestingly, the sublimation free energy is less significantly affected by neglecting thermal expansion because the systematic errors in the enthalpy and entropy cancel somewhat. Second, because solid state nuclear magnetic resonance (NMR) plays an increasingly important role in molecular crystal studies, this Account discusses how fragment methods can be used to achieve higher-accuracy chemical shifts in molecular crystals. Whereas widely used plane wave density functional theory models are largely restricted to generalized gradient approximation (GGA) functionals like PBE in practice, fragment methods allow the routine use of hybrid density functionals with only modest increases in computational cost. In extensive molecular crystal benchmarks, hybrid functionals like PBE0 predict chemical shifts with 20-30% higher accuracy than GGAs, particularly for ¹H, ¹³C, and ¹⁵N nuclei. Due to their higher sensitivity to polarization effects, ¹⁷O chemical shifts prove slightly harder to predict with fragment methods. Nevertheless, the fragment model results are still competitive with those from GIPAW. The improved accuracy achievable with fragment approaches and hybrid density functionals increases discrimination between different potential assignments of individual shifts or crystal structures, which is critical in NMR crystallography applications. This higher accuracy and greater discrimination are highlighted in application to the solid state NMR of different acetaminophen and testosterone crystal forms.

How Large Should the QM Region Be in QM/MM Calculations? The Case of Catechol O-Methyltransferase

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in studies of enzymatic catalysis. Until recently, it has been cost prohibitive to determine the asymptotic limit of key energetic and structural properties with respect to increasingly large QM regions. Leveraging recent advances in electronic structure efficiency and accuracy, we investigate catalytic properties in catechol O-methyltransferase, a prototypical methyltransferase critical to human health. Using QM regions ranging in size from reactants-only (64 atoms) to nearly one-third of the entire protein (940 atoms), we show that properties such as the activation energy approach within chemical accuracy of the large-QM asymptotic limits rather slowly, requiring approximately 500-600 atoms if the QM residues are chosen simply by distance from the substrate. This slow approach to asymptotic limit is due to charge transfer from protein residues to the reacting substrates. Our large QM/MM calculations enable identification of charge separation for fragments in the transition state as a key component of enzymatic methyl transfer rate enhancement. We introduce charge shift analysis that reveals the minimum number of protein residues (approximately 11-16 residues or 200-300 atoms for COMT) needed for quantitative agreement with large-QM simulations. The identified residues are not those that would be typically selected using criteria such as chemical intuition or proximity. These results provide a recipe for a more careful determination of QM region sizes in future QM/MM studies of enzymes.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state ¹³C and ¹⁵N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

Exploring the Dependence of QM/MM Calculations of Enzyme Catalysis on the Size of the QM Region

Although QM/MM calculations are the primary current tool for modeling enzymatic reactions, the reliability of such calculations can be limited by the size of the QM region. Thus, we examine in this work the dependence of QM/MM calculations on the size of the QM region, using the reaction of catechol-O-methyl transferase (COMT) as a test case. Our study focuses on the effect of adding residues to the QM region on the activation free energy, obtained with extensive QM/MM sampling. It is found that the sensitivity of the activation barrier to the size of the QM is rather limited, while the dependence of the reaction free energy is somewhat larger. Of course, the results depend on the inclusion of the first solvation shell in the QM regions. For example, the inclusion of the Mg²⁺ ion can change the activation barrier due to charge transfer effects. However, such effects can easily be included in semiempirical approaches by proper parametrization. Overall, we establish that QM/MM calculations of activation barriers of enzymatic reactions are not highly sensitive to the size of the QM region, beyond the immediate region that describes the reacting atoms.

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Solution-State (17)O Quadrupole Central-Transition NMR Spectroscopy in the Active Site of Tryptophan Synthase

Oxygen is an essential participant in the acid-base chemistry that takes place within many enzyme active sites, yet has remained virtually silent as a probe in NMR spectroscopy. Here, we demonstrate the first use of solution-state (17)O quadrupole central-transition NMR spectroscopy to characterize enzymatic intermediates under conditions of active catalysis. In the 143 kDa pyridoxal-5'-phosphate-dependent enzyme tryptophan synthase, reactions of the α-aminoacrylate intermediate with the nucleophiles indoline and 2-aminophenol correlate with an upfield shift of the substrate carboxylate oxygen resonances. First principles calculations suggest that the increased shieldings for these quinonoid intermediates result from the net increase in the charge density of the substrate-cofactor π-bonding network, particularly at the adjacent α-carbon site.