Calculation of chemical shift anisotropy in proteins

High-efficiency low-power 13C-15N cross polarization in MAS NMR

Biomolecular solid-state magic angle spinning (MAS) NMR spectroscopy frequently relies on selective 13C-15N magnetization transfers, for various kinds of correlation experiments. Introduced in 1998, spectrally induced filtering in combination with cross polarization (SPECIFIC-CP) is a selective heteronuclear magnetization transfer experiment widely used for biological applications. At MAS frequencies below 20 kHz, commonly used for 13C-detected MAS NMR experiments, SPECIFIC-CP transfer between amide 15N and 13Cα atoms (NCA) is typically performed with radiofrequency (rf) fields set higher than the MAS frequency for both 13C and 15N channels, and high-power 1H decoupling rf field is simultaneously applied. Here, we experimentally explore a broad range of NCA zero-quantum (ZQ) SPECIFIC-CP matching conditions at the MAS frequency of 14 kHz and compare the best high- and low-power matching conditions with respect to selectivity, robustness, and sensitivity at lower 1H decoupling rf fields. We show that low-power NCA SPECIFIC-CP matching condition gives rise to 20% sensitivity enhancement compared to high-power conditions, in 2D NCA spectra of microcrystalline assemblies of HIV-1 CACTD-SP1 protein with inositol hexakis-phosphate (IP6).

Molecular mechanisms and evolutionary robustness of a color switch in proteorhodopsins

Proteorhodopsins are widely distributed photoreceptors from marine bacteria. Their discovery revealed a high degree of evolutionary adaptation to ambient light, resulting in blue- and green-absorbing variants that correlate with a conserved glutamine/leucine at position 105. On the basis of an integrated approach combining sensitivity-enhanced solid-state nuclear magnetic resonance (ssNMR) spectroscopy and linear-scaling quantum mechanics/molecular mechanics (QM/MM) methods, this single residue is shown to be responsible for a variety of synergistically coupled structural and electrostatic changes along the retinal polyene chain, ionone ring, and within the binding pocket. They collectively explain the observed color shift. Furthermore, analysis of the differences in chemical shift between nuclei within the same residues in green and blue proteorhodopsins also reveals a correlation with the respective degree of conservation. Our data show that the highly conserved color change mainly affects other highly conserved residues, illustrating a high degree of robustness of the color phenotype to sequence variation.

Dynamic Coupling of Tyrosine 185 with the Bacteriorhodopsin Photocycle, as Revealed by Chemical Shifts, Assisted AF-QM/MM Calculations and Molecular Dynamic Simulations

Aromatic residues are highly conserved in microbial photoreceptors and play crucial roles in the dynamic regulation of receptor functions. However, little is known about the dynamic mechanism of the functional role of those highly conserved aromatic residues during the receptor photocycle. Tyrosine 185 (Y185) is one of the highly conserved aromatic residues within the retinal binding pocket of bacteriorhodopsin (bR). In this study, we explored the molecular mechanism of its dynamic coupling with the bR photocycle by automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) calculations and molecular dynamic (MD) simulations based on chemical shifts obtained by 2D solid-state NMR correlation experiments. We observed that Y185 plays a significant role in regulating the retinal cis–trans thermal equilibrium, stabilizing the pentagonal H-bond network, participating in the orientation switch of Schiff Base (SB) nitrogen, and opening the F42 gate by interacting with the retinal and several key residues along the proton translocation channel. Our findings provide a detailed molecular mechanism of the dynamic couplings of Y185 and the bR photocycle from a structural perspective. The method used in this paper may be applied to the study of other microbial photoreceptors.

Using quantum chemistry to estimate chemical shifts in biomolecules

An automated fragmentation quantum mechanics/molecular mechanics approach (AFNMR) has shown promising results in chemical shift calculations for biomolecules. Sample results for ubiquitin, and an RNA hairpin and helix are presented, and used to recent directions in quantum calculations. Trends in chemical shift are stable with regards to change in density functional or basis sets, and the use of the small "pcSseg-0" basis, which was optimized for chemical shift prediction [1], opens the way to more extensive conformational averaging, which can often be necessary, even for fairly well-defined structures.

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.

Accurate Backbone 13 C and 15 N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate 13 C and 15 N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for 15 N atoms. Here we compare experimentally determined backbone 13 Cα and 15 NH chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed 15 NH chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.

Functional roles of tyrosine 185 during the bacteriorhodopsin photocycle as revealed by in situ spectroscopic studies

Tyrosine 185 (Y185), one of the aromatic residues within the retinal (Ret) chromophore binding pocket in helix F of bacteriorhodopsin (bR), is highly conserved among the microbial rhodopsin family proteins. Many studies have investigated the functions of Y185, but its underlying mechanism during the bR photocycle remains unclear. To address this research gap, in situ two-dimensional (2D) magic-angle spinning (MAS) solid-state NMR (ssNMR) of specifically labelled bR, combined with light-induced transient absorption change measurements, dynamic light scattering (DLS) measurements, titration analysis and site-directed mutagenesis, was used to elucidate the functional roles of Y185 during the bR photocycle in the native membrane environment. Different interaction modes were identified between Y185 and the Ret chromophore in the dark-adapted (inactive) state and M (active) state, indicating that Y185 may serve as a rotamer switch maintaining the protein dynamics, and plays an important role in the efficient proton-pumping mechanism in the bR purple membrane.

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.

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.

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.

Quantifying protein dynamics in the ps-ns time regime by NMR relaxation

Both ¹⁵N chemical shift anisotropy (CSA) and sufficiently rapid exchange linebroadening transitions exhibit relaxation contributions that are proportional to the square of the magnetic field. Deconvoluting these contributions is further complicated by residue-dependent variations in protein amide ¹⁵N CSA values which have proven difficult to accurately measure. Exploiting recently reported improvements for the implementation of T₁ and T_1ρ experiments, field strength-dependent studies have been carried out on the B3 domain of protein G (GB3) as well as on the immunophilin FKBP12 and a H87V variant of that protein in which the major conformational exchange linebroadening transition is suppressed. By applying a zero frequency spectral density rescaling analysis to the relaxation data collected at magnetic fields from 500 to 900 MHz ¹H, differential residue-specific ¹⁵N CSA values have been obtained for GB3 which correlate with those derived from solid state and liquid crystalline NMR measurements to a level similar to the correlation among those previously reported studies. Application of this analysis protocol to FKBP12 demonstrated an efficient quantitation of both weak exchange linebroadening contributions and differential residue-specific ¹⁵N CSA values. Experimental access to such differential residue-specific ¹⁵N CSA values should significantly facilitate more accurate comparisons with molecular dynamics simulations of protein motion that occurs within the timeframe of global molecular tumbling.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Dynamic Water-Mediated Hydrogen Bonding in a Collagen Model Peptide

In the canonical (G-X-Y)(n) sequence of the fibrillar collagen triple helix, stabilizing direct interchain hydrogen bonding connects neighboring chains. Mutations of G can disrupt these interactions and are linked to connective tissue diseases. Here we integrate computational approaches with nuclear magnetic resonance (NMR) to obtain a dynamic view of hydrogen bonding distributions in the (POG)(4)(-)(POA)-(POG)(5) peptide, showing that the solution conformation, dynamics, and hydrogen bonding deviate from the reported X-ray crystal structure in many aspects. The simulations and NMR data provide clear evidence of inequivalent environments in the three chains. Molecular dynamics (MD) simulations indicate direct interchain hydrogen bonds in the leading chain, water bridges in the middle chain, and nonbridging waters in the trailing chain at the G → A substitution site. Theoretical calculations of NMR chemical shifts using a quantum fragmentation procedure can account for the unusual downfield NMR chemical shifts at the substitution sites and are used to assign the resonances to the individual chains. The NMR and MD data highlight the sensitivity of amide shifts to changes in the acceptor group from peptide carbonyls to water. The results are used to interpret solution NMR data for a variety of glycine substitutions and other sequence triplet interruptions to provide new connections between collagen sequences, their associated structures, dynamical behavior, and their ability to recognize collagen receptors.

Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals

First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.

Fragment-based (13)C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods

We assess the quality of fragment-based ab initio isotropic (13)C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic (13)C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.

AFNMR: automated fragmentation quantum mechanical calculation of NMR chemical shifts for biomolecules

We evaluate the performance of the automated fragmentation quantum mechanics/molecular mechanics approach (AF-QM/MM) on the calculation of protein and nucleic acid NMR chemical shifts. The AF-QM/MM approach models solvent effects implicitly through a set of surface charges computed using the Poisson-Boltzmann equation, and it can also be combined with an explicit solvent model through the placement of water molecules in the first solvation shell around the solute; the latter substantially improves the accuracy of chemical shift prediction of protons involved in hydrogen bonding with solvent. We also compare the performance of AF-QM/MM on proteins and nucleic acids with two leading empirical chemical shift prediction programs SHIFTS and SHIFTX2. Although the empirical programs outperform AF-QM/MM in predicting chemical shifts, the differences are in some cases small, and the latter can be applied to chemical shifts on biomolecules which are outside the training set employed by the empirical programs, such as structures containing ligands, metal centers, and non-standard residues. The AF-QM/MM described here is implemented in version 5 of the SHIFTS software, and is fully automated, so that only a structure in PDB format is required as input.

Correction of erroneously packed protein's side chains in the NMR structure based on ab initio chemical shift calculations

In this work, protein side chain (1)H chemical shifts are used as probes to detect and correct side-chain packing errors in protein's NMR structures through structural refinement. By applying the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method for ab initio calculation of chemical shifts, incorrect side chain packing was detected in the NMR structures of the Pin1 WW domain. The NMR structure is then refined by using molecular dynamics simulation and the polarized protein-specific charge (PPC) model. The computationally refined structure of the Pin1 WW domain is in excellent agreement with the corresponding X-ray structure. In particular, the use of the PPC model yields a more accurate structure than that using the standard (nonpolarizable) force field. For comparison, some of the widely used empirical models for chemical shift calculations are unable to correctly describe the relationship between the particular proton chemical shift and protein structures. The AF-QM/MM method can be used as a powerful tool for protein NMR structure validation and structural flaw detection.

Coupling of Conformational Transitions in the N-terminal Domain of the 51-kDa FK506-binding Protein (FKBP51) Near Its Site of Interaction with the Steroid Receptor Proteins

Interchanging Leu-119 for Pro-119 at the tip of the β4-β5 loop in the first FK506 binding domain (FK1) of the FKBP51 and FKBP52 proteins, respectively, has been reported to largely reverse the inhibitory (FKBP51) or stimulatory (FKBP52) effects of these co-chaperones on the transcriptional activity of glucocorticoid and androgen receptor-protein complexes. Previous NMR relaxation studies have identified exchange line broadening, indicative of submillisecond conformational motion, throughout the β4-β5 loop in the FK1 domain of FKBP51, which are suppressed by the FKBP52-like L119P substitution. This substitution also attenuates exchange line broadening in the underlying β2 and β3a strands that is centered near a bifurcated main chain hydrogen bond interaction between these two strands. The present study demonstrates that these exchange line broadening effects arise from two distinct coupled conformational transitions, and the transition within the β2 and β3a strands samples a transient conformation that resembles the crystal structures of the selectively inhibited FK1 domain of FKBP51 recently reported. Although the crystal structures for their series of inhibitors were interpreted as evidence for an induced fit mechanism of association, the presence of a similar conformation being significantly populated in the unliganded FKBP51 domain is more consistent with a conformational selection binding process. The contrastingly reduced conformational plasticity of the corresponding FK1 domain of FKBP52 is consistent with the current model in which FKBP51 binds to both the apo- and hormone-bound forms of the steroid receptor to modulate its affinity for ligand, whereas FKBP52 binds selectively to the latter state.

Quantum calculation of protein NMR chemical shifts based on the automated fragmentation method

The performance of quantum mechanical methods on the calculation of protein NMR chemical shifts is reviewed based on the recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. By using the Poisson-Boltzmann (PB) model and first solvation water molecules, the influence of solvent effect is also discussed. Benefiting from the fragmentation algorithm, the AF-QM/MM approach is computationally efficient, linear-scaling with a low pre-factor, and thus can be applied to routinely calculate the ab initio NMR chemical shifts for proteins of any size. The results calculated using Density Functional Theory (DFT) show that when the solvent effect is included, this method can accurately reproduce the experimental ¹H NMR chemical shifts, while the ¹³C NMR chemical shifts are less affected by the solvent. However, although the inclusion of solvent effect shows significant improvement for ¹⁵N chemical shifts, the calculated values still have large deviations from the experimental observations. Our study further demonstrates that AF-QM/MM calculated results accurately reflect the dependence of ¹³C(α) NMR chemical shifts on the secondary structure of proteins, and the calculated ¹H chemical shift can be utilized to discriminate the native structure of proteins from decoys.

Calculating nuclear magnetic resonance shieldings using systematic molecular fragmentation by annihilation

Systematic fragmentation accurately predicts theoretical chemical shieldings.

Correlation of chemical shifts predicted by molecular dynamics simulations for partially disordered proteins

There has been a longstanding interest in being able to accurately predict NMR chemical shifts from structural data. Recent studies have focused on using molecular dynamics (MD) simulation data as input for improved prediction. Here we examine the accuracy of chemical shift prediction for intein systems, which have regions of intrinsic disorder. We find that using MD simulation data as input for chemical shift prediction does not consistently improve prediction accuracy over use of a static X-ray crystal structure. This appears to result from the complex conformational ensemble of the disordered protein segments. We show that using accelerated molecular dynamics (aMD) simulations improves chemical shift prediction, suggesting that methods which better sample the conformational ensemble like aMD are more appropriate tools for use in chemical shift prediction for proteins with disordered regions. Moreover, our study suggests that data accurately reflecting protein dynamics must be used as input for chemical shift prediction in order to correctly predict chemical shifts in systems with disorder.

Accurate ab initio prediction of NMR chemical shifts of nucleic acids and nucleic acids/protein complexes

NMR chemical shift predictions based on empirical methods are nowadays indispensable tools during resonance assignment and 3D structure calculation of proteins. However, owing to the very limited statistical data basis, such methods are still in their infancy in the field of nucleic acids, especially when non-canonical structures and nucleic acid complexes are considered. Here, we present an ab initio approach for predicting proton chemical shifts of arbitrary nucleic acid structures based on state-of-the-art fragment-based quantum chemical calculations. We tested our prediction method on a diverse set of nucleic acid structures including double-stranded DNA, hairpins, DNA/protein complexes and chemically-modified DNA. Overall, our quantum chemical calculations yield highly/very accurate predictions with mean absolute deviations of 0.3–0.6 ppm and correlation coefficients (r²) usually above 0.9. This will allow for identifying misassignments and validating 3D structures. Furthermore, our calculations reveal that chemical shifts of protons involved in hydrogen bonding are predicted significantly less accurately. This is in part caused by insufficient inclusion of solvation effects. However, it also points toward shortcomings of current force fields used for structure determination of nucleic acids. Our quantum chemical calculations could therefore provide input for force field optimization.

Fragment quantum mechanical calculation of proteins and its applications

Conspectus The desire to study molecular systems that are much larger than what the current state-of-the-art ab initio or density functional theory methods could handle has naturally led to the development of novel approximate methods, including semiempirical approaches, reduced-scaling methods, and fragmentation methods. The major computational limitation of ab initio methods is the scaling problem, because the cost of ab initio calculation scales nth power or worse with system size. In the past decade, the fragmentation approach based on chemical locality has opened a new door for developing linear-scaling quantum mechanical (QM) methods for large systems and for applications to large molecular systems such as biomolecules. The fragmentation approach is highly attractive from a computational standpoint. First, the ab initio calculation of individual fragments can be conducted almost independently, which makes it suitable for massively parallel computations. Second, the electron properties, such as density and energy, are typically combined in a linear fashion to reproduce those for the entire molecular system, which makes the overall computation scale linearly with the size of the system. In this Account, two fragmentation methods and their applications to macromolecules are described. They are the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method and the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. The EE-GMFCC method is developed from the MFCC approach, which was initially used to obtain accurate protein-ligand QM interaction energies. The main idea of the MFCC approach is that a pair of conjugate caps (concaps) is inserted at the location where the subsystem is divided by cutting the chemical bond. In addition, the pair of concaps is fused to form molecular species such that the overcounted effect from added concaps can be properly removed. By introducing the electrostatic embedding field in each fragment calculation and two-body interaction energy correction on top of the MFCC approach, the EE-GMFCC method is capable of accurately reproducing the QM molecular properties (such as the dipole moment, electron density, and electrostatic potential), the total energy, and the electrostatic solvation energy from full system calculations for proteins. On the other hand, the AF-QM/MM method was used for the efficient QM calculation of protein nuclear magnetic resonance (NMR) parameters, including the chemical shift, chemical shift anisotropy tensor, and spin-spin coupling constant. In the AF-QM/MM approach, each amino acid and all the residues in its vicinity are automatically assigned as the QM region through a distance cutoff for each residue-centric QM/MM calculation. Local chemical properties of the central residue can be obtained from individual QM/MM calculations. The AF-QM/MM approach precisely reproduces the NMR chemical shifts of proteins in the gas phase from full system QM calculations. Furthermore, via the incorporation of implicit and explicit solvent models, the protein NMR chemical shifts calculated by the AF-QM/MM method are in excellent agreement with experimental values. The applications of the AF-QM/MM method may also be extended to more general biological systems such as DNA/RNA and protein-ligand complexes.

Cytochrome-P450-cytochrome-b5 interaction in a membrane environment changes 15N chemical shift anisotropy tensors

It has been well realized that the dependence of chemical shift anisotropy (CSA) tensors on the amino acid sequence, secondary structure, dynamics, and electrostatic interactions can be utilized in the structural and dynamic studies of proteins by NMR spectroscopy. In addition, CSA tensors could also be utilized to measure the structural interactions between proteins in a protein-protein complex. To this end, we report the experimentally measured backbone amide-(15)N CSA tensors for a membrane-bound 16.7 kDa full-length rabbit cytochrome-b5 (cytb5), in complexation with a 55.8 kDa microsomal rabbit cytochrome P450 2B4 (cytP4502B4). The (15)N-CSAs, determined using the (15)N CSA/(15)N-(1)H dipolar coupling transverse cross-correlated rates, for free cytb5 are compared with those for the cytb5 bound to cytP4502B4. An overall increase in backbone amide-(15)N transverse cross-correlated rates for the cytb5 residues in the cytb5-cytP450 complex is observed as compared to the free cytb5 residues. Due to fast spin-spin relaxation (T2) and subsequent broadening of the signals in the complex, we could measure amide-(15)N CSAs only for 48 residues of cytb5 as compared to 84 residues of free cytb5. We observed a change in (15)N CSA for most residues of cytb5 in the complex, as compared to free cytb5, suggesting a dynamic interaction between the oppositely charged surfaces of anionic cytb5 and cationic cytP450. The mean values of (15)N CSA determined for residues in helical, sheet, and turn regions of cytb5 in the complex are -184.5, -146.8, and -146.2 ppm, respectively, with an overall average value of -165.5 ppm (excluding the values from residues in more flexible termini). The measured CSA value for residues in helical conformation is slightly larger as compared to previously reported values. This may be attributed to the paramagnetic effect from Fe(III) of the heme in cytb5, which is similar to our previously reported values for the free cytb5.

Quantum Mechanical Study of Vicinal J Spin-Spin Coupling Constants for the Protein Backbone

We have performed densisty functional theory (DFT) calculations of vicinal J coupling constants involving the backbone torsional angle for the protein GB3 using our recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach (Xiao He et al. J. Phys. Chem. B 2009, 113, 10380-10388). Interestingly, the calculated values based on an NMR structure are more accurate than those based on a high-resolution X-ray strucure because the NMR structure was refined using a large number of residual dipolar couplings (RDCs) whereas the hydrogen atoms were added into the X-ray structure in idealized positions, confirming that the postioning of the hydrogen atoms relative to the backbone atoms is important to the accuracy of J coupling constant prediction. By comparing three Karplus equations, our results have demonstrated that hydrogen bonding, substituent and electrostatic effects could have significant impacts on vicinal J couplings even though they depend mostly on the intervening dihedral angles. The root-mean-square deviations (RMSDs) of the calculated (3)J(H(N),H(α)), (3)J(H(N),C(β)), (3)J(H(N),C') values based on the NMR structure are 0.52, 0.25, and 0.35 Hz, respectively, after taking the dynamic effect into consideration. The excellent accuracy demonstrates that our AF-QM/MM approach is a useful tool to study the relationship between J coupling constants and the structure and dynamics of proteins.

Conformational Sampling by Ab Initio Molecular Dynamics Simulations Improves NMR Chemical Shift Predictions

Car-Parrinello molecular dynamics simulations were performed for N-methyl acetamide as a small test system for amide groups in protein backbones, and NMR chemical shifts were calculated based on the generated ensemble. If conformational sampling and explicit solvent molecules are taken into account, excellent agreement between the calculated and experimental chemical shifts is obtained. These results represent a landmark improvement over calculations based on classical molecular dynamics (MD) simulations especially for amide protons, which are predicted too high-field shifted based on the latter ensembles. We were able to show that the better results are caused by the solute-solvents interactions forming shorter hydrogen bonds as well as by the internal degrees of freedom of the solute. Inspired by these results, we propose our approach as a new tool for the validation of force fields due to its power of identifying the structural reasons for discrepancies between the experimental and calculated data.

An extrapolation method for the efficient calculation of molecular response properties within Born-Oppenheimer molecular dynamics

The calculation of molecular response properties in dynamic molecular systems is a major challenge that requires sampling over many steps of, e.g., Born-Oppenheimer molecular dynamics (BO-MD) simulations. We present an extrapolation scheme to accelerate such calculations for multiple steps within BO-MD trajectories or equivalently within other sampling methods of conformational space. The extrapolation scheme is related to the one introduced by Pulay and Fogarasi [Chem. Phys. Lett., 2004, 386, 272] for self-consistent field (SCF) energy calculations. We extend the extrapolation to the quantities within our density matrix-based Laplace-transformed coupled perturbed SCF (DL-CPSCF) method that allows for linear-scaling calculations of response properties for large molecular systems. Here, we focus on the example of calculating NMR chemical shifts for which the number of required DL-CPSCF iterations reduces by roughly 40-70%.

Automated Fragmentation QM/MM Calculation of Amide Proton Chemical Shifts in Proteins with Explicit Solvent Model

We have performed a density functional theory (DFT) calculation of the amide proton NMR chemical shift in proteins using a recently developed automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. Systematic investigation was carried out to examine the influence of explicit solvent molecules, cooperative hydrogen bonding effects, density functionals, size of the basis sets, and the local geometry of proteins on calculated chemical shifts. Our result demonstrates that the predicted amide proton ((1)HN) NMR chemical shift in explicit solvent shows remarkable improvement over that calculated with the implicit solvation model. The cooperative hydrogen bonding effect is also shown to improve the accuracy of (1)HN chemical shifts. Furthermore, we found that the OPBE exchange-correlation functional is the best density functional for the prediction of protein (1)HN chemical shifts among a selective set of DFT methods (namely, B3LYP, B3PW91, M062X, M06L, mPW1PW91, OB98, OPBE), and the locally dense basis set of 6-311++G**/4-31G* is shown to be sufficient for (1)HN chemical shift calculation. By taking ensemble averaging into account, (1)HN chemical shifts calculated by the AF-QM/MM approach can be used to validate the performance of various force fields. Our study underscores that the electronic polarization of protein is of critical importance to stabilizing hydrogen bonding, and the AF-QM/MM method is able to describe the local chemical environment in proteins more accurately than most widely used empirical models.

Chemical shifts in biomolecules

NMR chemical shifts are sensitive probes of structure and dynamics in proteins. Empirical models, based on a large database of measured shifts, take an input structure and provide increasingly accurate estimates of the corresponding shifts. Quantum chemical calculations can provide the same information, with greater generality but (currently) with less accuracy. These methods are now providing new ways to approach NMR structure determination, and new insights into the conformational dynamics of proteins.

Multidimensional magic angle spinning NMR spectroscopy for site-resolved measurement of proton chemical shift anisotropy in biological solids

The proton chemical shift (CS) tensor is a sensitive probe of structure and hydrogen bonding. Highly accurate quantum-chemical protocols exist for computation of (1)H magnetic shieldings in the various contexts, making proton chemical shifts potentially a powerful predictor of structural and electronic properties. However, (1)H CS tensors are not yet widely used in protein structure calculation due to scarcity of experimental data. While isotropic proton shifts can be readily measured in proteins even in the solid state, determination of the (1)H chemical shift anisotropy (CSA) tensors remains challenging, particularly in molecules containing multiple proton sites. We present a method for site-resolved measurement of amide proton CSAs in fully protonated solids under magic angle spinning. The approach consists of three concomitant 3D experiments yielding spectra determined by either mainly (1)H CSA, mainly (1)H–(15)N dipolar, or combined (1)H CSA and (1)H–(15)N dipolar interactions. The anisotropic interactions are recoupled using RN-sequences of appropriate symmetry, such as R12(1)(4), and (15)N/(13)C isotropic CS dimensions are introduced via a short selective (1)H–(15)N cross-polarization step. Accurate (1)H chemical shift tensor parameters are extracted by simultaneous fit of the lineshapes recorded in the three spectra. An application of this method is presented for an 89-residue protein, U-(13)C,(15)N-CAP-Gly domain of dynactin. The CSA parameters determined from the triple fits correlate with the hydrogen-bonding distances, and the trends are in excellent agreement with the prior solution NMR results. This approach is generally suited for recording proton CSA parameters in various biological and organic systems, including protein assemblies and nucleic acids.

Quantum chemical calculations of amide-15N chemical shift anisotropy tensors for a membrane-bound cytochrome-b5

There is considerable interest in determining amide-(15)N chemical shift anisotropy (CSA) tensors from biomolecules and understanding their variation for structural and dynamics studies using solution and solid-state NMR spectroscopy and also by quantum chemical calculations. Due to the difficulties associated with the measurement of CSA tensors from membrane proteins, NMR-based structural studies heavily relied on the CSA tensors determined from model systems, typically single crystals of model peptides. In the present study, the principal components of backbone amide-(15)N CSA tensors have been determined using density functional theory for a 16.7 kDa membrane-bound paramagnetic heme containing protein, cytochrome-b(5) (cytb(5)). All the calculations were performed by taking residues within 5 Å distance from the backbone amide-(15)N nucleus of interest. The calculated amide-(15)N CSA spans agree less well with our solution NMR data determined for an effective internuclear distance r(N-H) = 1.023 Å and a constant angle β = 18° that the least shielded component (δ(11)) makes with the N-H bond. The variation of amide-(15)N CSA span obtained using quantum chemical calculations is found to be smaller than that obtained from solution NMR measurements, whereas the trends of the variations are found to be in close agreement. We believe that the results reported in this study will be useful in studying the structure and dynamics of membrane proteins and heme-containing proteins, and also membrane-bound protein-protein complexes such as cytochromes-b5-P450.

Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 3. Conformational Sampling and Explicit Solvents Model

Fragment-based quantum chemical calculations are able to accurately calculate NMR chemical shifts even for very large molecules like proteins. But even with systematic optimization of the level of theory and basis sets as well as the use of implicit solvents models, some nuclei like polar protons and nitrogens suffer from poor predictions. Two properties of the real system, strongly influencing the experimental chemical shifts but almost always neglected in the calculations, will be discussed here in great detail: (1) conformational averaging and (2) interactions with first-shell solvent molecules. Classical molecular dynamics simulations in explicit water were carried out for obtaining a representative ensemble including the arrangement of neighboring solvent molecules, which was then subjected to quantum chemical calculations. We could demonstrate with the small test system N-methyl acetamide (NMA) that the calculated chemical shifts show immense variations of up to 6 ppm and 50 ppm for protons and nitrogens, respectively, depending on the snapshot taken from a classical molecular dynamics simulation. Applying the same approach to the HA2 domain of the influenza virus glycoprotein hemagglutinin, a 32-amino-acid-long polypeptide, and comparing averaged values to the experiment, chemical shifts of nonpolar protons and carbon atoms in proteins were calculated with unprecedented accuracy. Additionally, the mean absolute error could be reduced by a factor of 2.43 for polar protons, and reasonable correlations were obtained for nitrogen and carbonyl carbon in contrast to all other studies published so far.

Determination of 15N chemical shift anisotropy from a membrane-bound protein by NMR spectroscopy

Chemical shift anisotropy (CSA) tensors are essential in the structural and dynamic studies of proteins using NMR spectroscopy. Results from relaxation studies in biomolecular solution and solid-state NMR experiments on aligned samples are routinely interpreted using well-characterized CSA tensors determined from model compounds. Since CSA tensors, particularly the (15)N CSA, highly depend on a number of parameters including secondary structure, electrostatic interaction, and the amino acid sequence, there is a need for accurately determined CSA tensors from proteins. In this study, we report the backbone amide-(15)N CSA tensors for a 16.7-kDa membrane-bound and paramagnetic-heme containing protein, rabbit Cytochrome b(5) (cytb(5)), determined using the (15)N CSA/(15)N-(1)H dipolar transverse cross-correlation rates. The mean values of (15)N CSA determined for residues in helical, sheet, and turn regions are -187.9, -166.0, and -161.1 ppm, respectively, with an overall average value of -171.7 ppm. While the average CSA value determined from this study is in good agreement with previous solution NMR experiments on small globular proteins, the CSA value determined for residues in helical conformation is slightly larger, which may be attributed to the paramagnetic effect from Fe(III) of the heme unit in cytb(5). However, like in previous solution NMR studies, the CSA values reported in this study are larger than the values measured from solid-state NMR experiments. We believe that the CSA parameters reported in this study will be useful in determining the structure, dynamics, and orientation of proteins, including membrane proteins, using NMR spectroscopy.

Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 2. Level of Theory, Basis Set, and Solvents Model Dependence

It has been demonstrated that the fragmentation scheme of our adjustable density matrix assembler (ADMA) approach for the quantum chemical calculations of very large systems is well-suited to calculate NMR chemical shifts of proteins [ Frank et al. Proteins2011, 79, 2189-2202 ]. The systematic investigation performed here on the influences of the level of theory, basis set size, inclusion or exclusion of an implicit solvent model, and the use of partial charges to describe additional parts of the macromolecule on the accuracy of NMR chemical shifts demonstrates that using a valence triple-ζ basis set leads to large improvement compared to the results given in the previous publication. Additionally, moving from the B3LYP to the mPW1PW91 density functional and including partial charges and implicit solvents gave the best results with mean absolute errors of 0.44 ppm for hydrogen atoms excluding H(N) atoms and between 1.53 and 3.44 ppm for carbon atoms depending on the size and also on the accuracy of the protein structure. Polar hydrogen and nitrogen atoms are more difficult to predict. For the first, explicit hydrogen bonds to the solvents need to be included and, for the latter, going beyond DFT to post-Hartree-Fock methods like MP2 is probably required. Even if empirical methods like SHIFTX+ show similar performance, our calculations give for the first time very reliable chemical shifts that can also be used for complexes of proteins with small-molecule ligands or DNA/RNA. Therefore, taking advantage of its ab initio nature, our approach opens new fields of application that would otherwise be largely inaccessible due to insufficient availability of data for empirical parametrization.

Fragment density functional theory calculation of NMR chemical shifts for proteins with implicit solvation

Fragment density functional theory (DFT) calculation of NMR chemical shifts for several proteins (Trp-cage, Pin1 WW domain, the third IgG-binding domain of Protein G (GB3) and human ubiquitin) has been carried out. The present study is based on a recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach but the solvent effects are included by using the PB (Poisson-Boltzmann) model. Our calculated chemical shifts of (1)H and (13)C for these four proteins are in excellent agreement with experimentally measured values and represent clear improvement over that from the gas phase calculation. However, although the inclusion of the solvent effect also improves the computed chemical shifts of (15)N, the results do not agree with experimental values as well as (1)H and (13)C. Our study also demonstrates that AF-QM/MM calculated results accurately reproduce the separation of α-helical and β-sheet chemical shifts for (13)C(α) atoms in proteins, and using the (1)H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable.