Keywords

1 Introduction

Nuclear magnetic resonance (NMR) spectroscopy is an invaluable and widely used technique in areas of chemistry, biology and medicine [1, 2]. In proteins, the chemical shift tensors are key parameters in the NMR experiment, enabling signals from different nuclei of any given type in a molecule to be distinguished. During the past decades, there has been significant progress in using chemical shift information for characterization of protein structure and dynamics [3–11].

Although the chemical shifts are probably the most precise parameters that can be obtained for biomolecules, the inherently complex dependency on geometric, dynamic and electronic properties has made accurate calculation of chemical shifts of protein a significant challenge [12–14]. There are mainly two widely used methods to calculate protein NMR chemical shifts: the empirical approach based on the experimental database and the ab initio approach based on quantum mechanical (QM) calculations. Empirical methods rely on statistical data derived from a limited set of high-quality 3D structures and make use of empirical or semi-empirical equations to account for the non-sequential environment [15–19]. These methods are usually quite successful in predicting backbone chemical shifts, which are primarily determined by the local secondary structure, but they are not so well suited to handle proteins with nonstandard residues, metal cofactors, or protein-ligand complexes.

Over the past decade, QM methods have become increasingly useful for NMR chemical shift studies. Following the pioneering work of de Dios et al. [20–22], a number of quantum calculations have been carried out for chemical shifts in proteins and peptides [23–33]. However, due to the poor scaling of ab initio and DFT methods, it has not been practical to apply standard all-electron quantum chemistry methods to realistic macromolecules. In fact, full quantum mechanical computations on structures with 1,000 atoms or more are currently not routinely feasible. Fortunately, many previous studies have proven that there is no need to include all atoms in the QM NMR calculation because the nuclear shielding is fundamentally a local physical property. Cui and Karplus proposed a method for calculating chemical shifts in the QM/MM framework, and concluded that the QM/MM method can provide good descriptions of the environmental effect on chemical shifts [34]. Frank et al. calculated the chemical shifts using the fragment based adjustable density matrix assembler (ADMA) method [35–37]. Gao et al. also reported a fragment molecular orbital (FMO) method for NMR chemical shift calculations at the Hartree-Fock level [38, 39]. In our previous studies [40, 41, 49], a more efficient automated fragmentation quantum mechanics/molecular mechanics approach (AF-QM/MM) was shown to be applicable to routine ab initio NMR chemical shift calculation for proteins of any size. In this approach, the entire protein is divided into individual fragments, and residues within a certain buffer region surrounding each fragment are included in the QM calculation to preserve the chemical environment of the divided fragment. The remainder of the system outside the buffer regions is described by the MM method. The AF-QM/MM calculated NMR chemical shifts of several proteins are in good agreement with the experimental measurement [40, 41].

Since most NMR measurements are performed on liquid samples, the NMR parameters (in particular NMR chemical shifts) are highly sensitive to the molecular environment, and especially the solvent effect. The effect of solvent on nuclear magnetic shielding parameters derived from NMR spectroscopy has been of great interest for a long time [42–47]. Several empirical approaches have been formulated to evaluate the solvent effects on nuclear shieldings, however, the development of ab initio calculation of NMR properties of proteins in solution has only recently received attention, and most of the studies were focused on small molecular structures or model peptides. In this review, we mainly discuss the influence of solvent effects on the QM calculation of protein NMR chemical shifts, by including both the implicit and explicit solvent model based on our previous works [40, 41, 48, 49].

2 Automated Fragmentation QM/MM Method

2.1 Fragmentation Criteria

The basic fragmentation scheme in the AF-QM/MM approach is shown in Fig. 5.1. In this approach, the entire protein system is divided into non-overlapping fragments termed core regions. The residues within a certain range from the core region are assigned as the buffer region. Both the core region and its buffer region are treated by QM, whereas the rest of the system is described by an empirical point-charge model. The purpose of the buffer area is to include the local QM effects on the chemical shifts. Each fragment-centric QM/MM calculation is carried out separately. Only the shielding constants of the atoms in the core region are extracted from the individual QM/MM calculations. A more detailed illustration of the automated fragmentation scheme is presented in Fig. 5.2.

Fig. 5.1
figure 1

Subsetting scheme for the AF-QM/MM approach

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Fig. 5.2
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a Definition of the residue unit used in this work. b Nth amino acid is the core region. Sequentially connected (n − 2)th, (n − 1)th, (n + 1)th and (n + 2)th residues are included in the buffer region. In addition, the residues in spatial contact with the nth residue are also assigned to the buffer region (see text for further details)

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For proteins discussed in this work, each residue is taken as the core region. A different definition of the residue that consists of the –CO–NH–CHR– is adopted to preserve the electron delocalization across the peptide bond (Fig. 5.2a). A generalized molecular cap was also introduced to take into account the QM polarization effect and charge transfer within the first shell from the residue of interest, as shown in Fig. 5.2b. In this and all our previous studies, we adopt the following distance-dependent criteria to include residues within the buffer region of each core residue: (1) if one atom of the residue outside the core region is less than 4 Å away from any atom in the core region and at least one of the two atoms is a non-hydrogen atom; (2) if the distance between one hydrogen atom in the core region and the other hydrogen atom outside the core region is less than 3 Å, or (3) if a heavy atom on an aromatic ring is within 5 Å from any atom in the core region. Of course, other distance-dependent criteria could be used to further optimize the choice of the buffer region. The non-neighboring residues in the buffer region are simply capped by hydrogen atoms to construct the closed-shell fragment.

The remaining atoms beyond the buffer region are treated by MM method. A point-charge model is employed to account for the empirical electrostatic field outside the QM region. We use the full point charges for those junction atoms that are replaced by hydrogen atoms. Because a buffer region is added to smoothly link the core region and MM environment, atoms on the boundary between the QM and MM regions are relatively far from the core region and their influence is attenuated. By using a general criterion to assign a buffer zone to each residue, we can reduce the size of each fragment in order to make the QM calculation as small as possible until we strike a compromise between the desired accuracy and the computational cost. Although the total number of residue pairs is proportional to the square of the number of residues, the size of each fragment is independent of the overall protein size because each residue can have only a limited number of residues in its vicinity. Hence, the largest fragment normally contains less than 250 atoms consisting of C, H, O, N, and S, which is an affordable calculation at the HF and DFT levels. In this work, all the QM calculation were performed using Gaussian09 program [50].

2.2 Solvent Effects

The main obstacle of including solvent effects in QM/MM NMR calculation is the determination of solvent positions around the biomolecules. It is known that the interaction of the biomolecule with solvent is not well represented by the coordinates present in the experimental structures. There are no water molecules in the protein structure obtained by NMR experiment, and even some “crystallographic” waters are present in the X-ray structure, they represent only a fraction of the waters surrounding the biomolecule. In addition, the static positions of water molecules are probably not representative of the environment seen by the atoms of the solvated biomolecule. Therefore, in most of the calculations, the implicit continuum solvation model was used.

In continuum solvation model, the solute (protein) is represented by a charge distribution ρ(r) embedded in a cavity surrounded by a polarizable medium with dielectric constant ε. The solute charge distribution polarizes the dielectric medium and creates a reaction field which acts back to polarize the solute until equilibrium is reached. The reaction field acting on the solute can be effectively represented by that of induced charges on the cavity surface according to the classical electrostatic theory. In the current approach, we use the DivCon [51] program which combines the linear-scaling divide-and-conquer semi-empirical algorithm with the Poisson-Boltzmann (PB) equation to perform the self-consistent reaction field (SCRF) calculation. The CM2 charges for the atoms of proteins in conjunction with the PM3 methods were derived since the PM3/CM2 is one of the best polarizable charge models for NMR chemical shift calculations, as observed previously for HF/6-31G** and B3LYP/6-31G** calculations [41]. Then the set of point charges of the MM environment and on the molecular surface which represents the reaction field is used as the background charges in the QM calculation. The effective surface charges representing the solvent effects are shown in Fig. 5.3.

Fig. 5.3
figure 3

NMR structure of Trp cage (PDB entry: 1L2Y) together with the surface charges calculated by DivCon (red and blue dots represent the positive and negative charges, respectively)

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3 Applications

3.1 Comparison with the Full System Quantum Chemistry Calculations

Firstly, the AF-QM/MM method with the solvation model was used to compute the 1H, 13C and 15N absolute chemical shielding tensors of a small protein Trp-cage (20 residues, PDB entry: 1L2Y). And the results are compared with the conventional full system calculations as shown in Fig. 5.4.

Fig. 5.4
figure 4

Root mean square error (RMSE), mean unsigned error (MUE) and maximum error (MaxE) of AF-QM/MM with respect to the full system calculated 1H, 13C and 15N chemical shifts in Trp-cage at the B3LYP/6-31G** level

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In the full system calculation, the protein is computed as an intact molecule with the presence of the same set of surface charges. As one can see from Fig. 5.4, the root mean square errors (RMSEs) for the 1H, 13C and 15N are only 0.06, 0.22 and 0.55 ppm, respectively. All these errors are very small as all of them are less than 1 % of the absolute chemical shielding tensor. The result clearly demonstrates that, as expected, the AF-QM/MM calculated chemical shifts can well reproduce the full quantum mechanical calculations for proteins.

3.2 1H Chemical Shifts in Proteins

Proton chemical shifts are the most important and most studied output of NMR experiments. In proteins, the proton atoms can be divided into two categories. One is called non-polar 1H atoms which usually form covalent bonds with C atoms; the other group is called polar 1H atoms which usually from covalent bonds with polar N, S or P atoms, and most of them are involved in hydrogen bonding interactions. The measured chemical shifts of 1H atoms for these two groups are quite different. In this section, we first compare the non-polar 1H chemical shift of Trp-cage calculated by the AF-QM/MM method with the experimental values. For the hydrogen atoms, calculations in both gas phase and solution phase give excellent agreement with the experimental value as shown in Fig. 5.5a.

Fig. 5.5
figure 5

Correlation between experimental and calculated 1H NMR chemical shifts. a Trp-cage, b Pin1 WW domain. The exchangeable protons were excluded

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The RMSE, MUE, correlation coefficient and the fitted function are given in Table 5.1. Although the calculated results for trp-cage in the gas phase are pretty well, the inclusion of the solvent effects still improves the correlation between the theoretical and experimental values from 0.977 to 0.986. The RMSE also decreased from 0.39 to 0.29 ppm, and the slop of the correlation function is closer to 1. The results here show that the solvent effects are important and calculated NMR chemical shifts with the solvation model for 1H atom clearly improve the agreement between theory and experiment.

Table 5.1 Comparison of AF-QM/MM and experimental chemical shifts for the 1H atoms in Trp-cage and Pin1 WW domain
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We also calculated the non-polar 1H chemical shifts of Pin1 WW domain (PDB entry: 1PIN) which mainly consists of β-sheets. The comparison of our calculated chemical shifts with the experimental values is given in Fig. 5.5b and Table 5.1. Here, the similar result as that of trp-cage is observed. The theoretical 1H chemical shift in solvation is better correlated with the experimental values than results from gas-phase calculations. The RMSE using the solvent model is 0.42 ppm, which is smaller than the gas phase result of 0.57 ppm and the correlation between theoretical and experimental values also improved from 0.964 to 0.979. Thus, the inclusion of the solvent effects clearly improves the theoretical result. In our previous study [40], we also performed calculations on a large protein with mixed α-helical and β-sheet secondary structures, GB3 (PDB entry: 1IGD, 61 residues). The comparison between theoretical and experimental result is also shown in Table 5.1. Again, better correlation with experiment is seen for non-polar 1H chemical shift with the inclusion of solvation.

Furthermore, we check the performance of the AF-QM/MM method on the polar hydrogen especially for protein amide H atoms. The 1HN chemical shift is one of the most precise NMR parameters that can be measured, which plays key roles in peak assignments. Thus, a QM model that can accurately predict their chemical shift is in demand. Previous studies have found that the main reason for the inaccuracy in computed amide H chemical shifts arises from the improper treatment of the solvation effect, especially the specific solvent-solute hydrogen bond effect. To include these effects in the calculation, explicit inclusion of solvent molecules is required. In our previous study [49], we used a 3D reference interaction site model (3D-RISM) to correct the distribution of explicit solvent molecules. The algorithm of 3D-RISM method is based on statistical mechanics and has been shown to accurately reproduce water distributions at a reduced computational cost. The PLACEVENT [52, 53] program developed by Hirata and co-workers was utilized to translate the continuous distributions to explicit water molecules. In the calculation, only the water molecules in the first and second solvation shell (within 6.0 Å from any atom in the protein) are regarded as part of the entire system. While the implicit solvent model was used to represent the bulk solvent effect beyond the second solvent shell as shown in Fig. 5.6 [49].

Fig. 5.6
figure 6

Graphical representation of GB3 (PDB entry: 2IGD) together with the first, second solvation shells and surface charges calculated by DivCon program [51]. (Red and blue dots represent the positive and negative surface charges, respectively)

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The protein GB3 is taken as the initial geometry. Besides the crystallographic water, 678 more water molecules were added by the PLACEVENT program to mimic the first and second solvent shell. Calculated 1HN chemical shifts using both the explicit and implicit solvent models are compared in Fig. 5.7. As can be seen, the inclusion of explicit water molecules gives considerably better agreement with experiment over the implicit solvent model. The correlation coefficient (R) between the theoretical and experimental values is improved from 0.673 to 0.835. The RMSE is also decreased from 1.19 to 0.86 ppm. Table 5.2 lists those residues which have amide protons forming hydrogen bonds (H-bonds) with water molecules. It can be seen that those calculated 1HN chemical shifts using the pure implicit solvent model show large upfield shifts as compared to experimental values.

Fig. 5.7
figure 7

Correlation between the experimental and calculated 1HN chemical shifts of GB3 using the AF-QM/MM method (the QM level is at B3LYP/6-31G**). (red circle 1HN chemical shifts calculated using the implicit solvent model; blue circle 1HN chemical shift calculated using the explicit solvent model.)

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Table 5.2 Comparison of the experimental and AF-QM/MM calculated 1HN chemical shifts (in ppm) of GB3 for residues which form hydrogen bonds with water molecules using the explicit and implicit solvent models, respectively
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When the explicit solvents were included in the fragment QM calculations, the results show significant improvement. It clearly indicates that hydrogen bonding has large electronic polarization effect on the 1HN chemical shift (up to 2–3 ppm). The water molecule which forms direct H-bond with the amide proton in proteins should be treated quantum mechanically to accurately reproduce the experimental 1HN chemical shifts.

As shown in Fig. 5.7, although the inclusion of explicit water molecules improves the results, the calculated 1HN chemical shifts with the explicit solvent model are systematically underestimated by about 0.5 ppm. Previous studies on some model systems have illustrated that the cooperative hydrogen bonding effect has a non-negligible influence on 1HN chemical shifts by affecting the primary hydrogen bond geometry and polarizing the electron density around the amide proton. Therefore, we further explored the cooperative hydrogen bond effect on the protein 1HN chemical shifts. For simplicity, we took the N-methylacetamide (NMA) as the central fragment, the cooperative hydrogen bonding effects caused by both water and NMA molecules were investigated. As shown in Fig. 5.8, when the cooperative hydrogen bond was formed, the chemical shifts of the 1HN atom in the central residue are downfielded by around 0.3–0.5 ppm as opposed to the case of single H-bond. Therefore, we expand our definition of the buffer region to include the secondary hydrogen bond acceptor (the whole residue or water molecule) in the QM region. As depicted in Fig. 5.9, if the 1HN chemical shift in the core residue (A) is to be calculated and there is a cooperative hydrogen bond across the peptide bonds of residues: A, B (primary H-bond acceptor) and C (secondary H-bond acceptor), we also include residue C in the buffer region.

Fig. 5.8
figure 8

The 1HN chemical shift of the central fragment (A) as a function of the 1HN-O distance between fragment A and B calculated at the B3LYP/6-311++G** level. Left panel both the primary and secondary hydrogen bond acceptors are water molecules; right panel both the primary and secondary hydrogen bond acceptors are N-methylacetamides (NMAs). The H-bond length between fragment B and C are fixed at the original optimized structure at the B3LYP/6-31G** level (1.98 Ǻ for WAT-WAT and 2.09 Ǻ for NMA-NMA, respectively.)

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Fig. 5.9
figure 9

Subsetting scheme for the AF-QM/MM-PB approach with the explicit solvent model. The red and blue region represents the core and buffer region, respectively. On top of the original definition of the buffer region described in Ref. [41], this study adds one additional criterion which is including the secondary hydrogen bond acceptor (residue C) in the buffer region to take cooperative hydrogen bonding effect into account. The rest of the protein and explicit solvent molecules are described by point charges. The bulk solvent effect is described by the classical electrostatic potential induced by the point charges on the cavity surface calculated using the PB model

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The other factors that may govern the accuracy of calculated 1HN chemical shifts include the density functional and the size of basis set chosen in our calculation. Previous studies on small organic molecules have demonstrated that, at least a triple-zeta basis set with the diffuse basis function should be utilized to accurately reproduce the experimental amide hydrogen chemical shift. However, the computational cost is very demanding to apply large basis sets on the entire QM region consisting of normally 150–300 atoms, which is the normal size of each fragment (core + buffer region) using the current definition of the buffer region. Hence, the use of locally dense basis sets, i.e. the combination of two basis sets where the larger one is used for the atoms of interest and the smaller one for all the other atoms, is adopted. The 6-311++G** basis set was employed on the –CO–NH– atoms in both the core residue and other residues involved in the primary and secondary H-bonds (as illustrated in Fig. 5.9). If the H-bond acceptor is a water molecule, the entire water molecule is treated with the 6-311++G** basis set, while the rest atoms in the QM region are set to a smaller basis set. In this work, the 4-31G* basis set has been utilized and the result is shown in Fig. 5.10.

Fig. 5.10
figure 10

Correlation between experimental and calculated 1HN chemical shifts of GB3 using the AF-QM/MM method (the QM level is at B3LYP/6-311++G**/4-31G*)

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As can be seen, the inclusion of cooperative hydrogen bond effect and applying the locally dense basis set give remarkable improvement for the 1HN chemical shifts (compare Fig. 5.10 with Fig. 5.7). The calculation with the B3LYP/6-311++G**/4-31G* method decreases the RMSE from 0.86 to 0.49 ppm. In our previous study [49], we found that the increase of the lower basis set from 4-31G* to 6-31G* or 6-311G** does not reduce the overall RMSE for GB3. Hence, we conclude that the B3LYP functional with the mixed basis set of 6-311++G**/4-31G* strikes a compromise between the computational cost and attained accuracy.

3.3 13C and 15N Chemical Shifts in Proteins

Taking protein GB3 as an example, we also show the influence of solvation effects on the NMR chemical shifts of 13C. The comparison between theoretical and experimental result is shown in Fig. 5.11.

Fig. 5.11
figure 11

Correlation between the experimental and calculated 13C chemical shifts of GB3 using the AF-QM/MM method (the QM level is at B3LYP/6-31G**) (red circle 13C chemical shifts calculated in the gas phase; blue circle 13C chemical shifts calculated using the implicit solvent model)

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It is not surprising that, as shown in Fig. 5.11, the chemical shift of 13C atom is not significantly influenced by including the solvent effects, with the correlation coefficient of 0.994 in gas phase and 0.998 in implicit solvent. This is mainly because the 13C chemical shifts span a large range from aliphatic region (15–35 ppm) to the carbonyl region (170–180 ppm). To further analyze the result in more details, we also plot the chemical shift of 13Cα in Fig. 5.12.

Fig. 5.12
figure 12

Correlation between the experimental and calculated 13Cα chemical shifts of GB3 using the AF-QM/MM method (red circle 13Cα chemical shifts calculated in the gas phase at the B3LYP/6-31G** level; blue circle 13Cα chemical shifts calculated using the implicit solvent model at the B3LYP/6-31G** level; magenta circle 13Cα chemical shifts calculated using the explicit solvent model at the B3LYP/6-311++G**/4-31G* level)

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As shown in Fig. 5.12, the inclusion of the implicit solvation model shows some improvement and the overall correlation with experiment increased from 0.858 to 0.889 for GB3, and the RMSE was reduced from 2.89 to 2.41 ppm, but the influence is not very significant. That is mainly because most of the Cα atoms are buried in the hydrophobic core region of the protein and are nonpolar, their chemical shifts are less affected by the solvent. The errors of the calculated 13Cα chemical shifts with respect to the experimental values are likely due to the insufficient sampling of the protein structure, since the experimental observed chemical shifts represent the ensemble-averaged values. When the explicit waters were included, the calculated results did not show any improvement and the calculated 13Cα chemical shifts using the 6-311++G** basis set are all clearly underestimated with respect to the experimental values. Similar findings have also been concluded in the previous study by Case and co-workers [28].

The 15N results are summarized in Fig. 5.13. It has long been known that the 15N chemical shift in protein presents a challenge for first principle prediction because they are very sensitive to the chemical environment and are influenced by numerous factors. To accurately predict the 15N NMR chemical shifts usually requires high-level electron correlation methods beyond DFT.

Fig. 5.13
figure 13

Correlation between experimental and calculated 15N chemical shifts of GB3 using the AF-QM/MM method (red circle 15N chemical shifts calculated in the gas phase at the B3LYP/6-31G** level; blue circle 15N chemical shifts calculated using the implicit solvent model at the B3LYP/6-31G** level; magenta circle 15N chemical shifts calculated using the explicit solvent model at the B3LYP/6-311++G**/4-31G* level)

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From the B3LYP/6-31G** calculation, the correlation (R) between the calculated and experimental 15N chemical shifts is only 0.735 for GB3 in the gas phase. Although the inclusion of solvent effects shows significant improvement (with the correlation of 0.842 for GB3), it still has large deviations from the experimental values. As one can see from Fig. 5.13, the implicit solvation treatment on the nitrogen atoms improves more significantly than the nonpolar Cα atoms. However, as discussed in our previous study [40], there is a difference between backbone and side chain nitrogen atoms. For backbone amide nitrogen, which is buried in the core region of protein, the solvent effects on the 15N chemical shift are relatively weak, and the calculated shifts are usually larger than the experimentally measured values [40]. In contrast, solvent effects on the nitrogen atoms from the side chain amine groups (mostly exposed to the solvent) are stronger. However, as shown in Fig. 5.13, including explicit water molecules did not give much improvement. The correlation coefficient is marginally increased from 0.842 to 0.874. Besides the solvent effect, there are other factors which may govern the accuracy of theoretical prediction on 15N NMR chemical shifts, such as conformational sampling, the choice of DFT functionals, etc. Research along these lines is currently underway in our laboratory.

3.4 Probing the Secondary Structures of Proteins by the AF-QM/MM Method

In structural biology, the protein chemical shift is a powerful tool for studying the structure and dynamics of the protein. They are often used to predict regions of secondary structure in native and nonnative states of proteins, to aid the refinement of complex structures and characterization of conformational changes. Here we validated the capability of using the 13Cα secondary chemical shifts (i.e. the calculated chemical shifts in the native structure minus the random coil values) calculated by AF-QM/MM approach to distinguish the α-helix and β-sheet structures. The 13Cα random coil chemical shifts are taken from the CamCoil module [54]. The calculated results are presented in Fig. 5.14. As expected, there is a clear separation between the shieldings of the two secondary structure types. The 13Cα chemical shift experiences a downfield shift with an average value of 2.55 ppm (with respect to the random coil value) when in a helical configuration and a comparable upfield shift of −2.38 ppm in average when in β-sheet configuration. It shows that the AF-QM/MM method accurately reflects the influence of the local geometry on the chemical shift calculation.

Fig. 5.14
figure 14

Histograms of secondary shift (the calculated chemical shifts in the native structure minus the random coil values) distribution of α-helical and β-sheet chemical shifts for 13Cα in four proteins (Trp-cage, Pin1 WW domain, GB3 and ubiquitin)

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Recent studies [3, 6] have reported that, in combination with traditional molecular mechanical force field or de novo protein structure sampling techniques, protein structures can be derived using 1H, 13C and 15N NMR chemical shifts. Hence, we also used the 1H chemical shifts calculated by the AF-QM/MM method in detecting misfolded proteins relative to the natively folded target protein. The X-ray structure of Pin1 WW domain was taken as the native structure and a set of decoy structures for the same amino acid sequence was generated using Rosetta program. Figure 5.15 gives the correlation between calculated and experimental measured chemical shifts versus backbone RMSD with respect to the X-ray structure. As indicated, with the increase of the backbone RMSD, the NMR chemical shift correlation is declined. The RMSD values with the lowest correlations are far from the native structure. The results show that using the chemical shifts to detect the native structure from a collection of decoys is quite remarkable and would have significant potential in this regard.

Fig. 5.15
figure 15

Correlation between the experimental and calculated 1H chemical shifts versus backbone RMSD for Pin1 WW domain (PDB entries for the X-ray structure and NMR structures are 1PIN and 1I6C, respectively)

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4 Conclusions

In this review, we discussed the performance of QM methods on the calculation of protein chemical shifts based on the recently developed AF-QM/MM approach. By using the PB model and first solvation water molecules, the influence of solvent effect is also explored. Benefit from the fragment algorithm, the AF-QM/MM approach is computationally efficient and linear-scaling with a low pre-factor. The calculation for each residue takes about 2–4 h of computer time using the current definition of the buffer region. The approach is massively parallel and can be applied to routinely calculate the ab initio NMR chemical shifts for proteins of any size.

The calculated results also indicate that when the solvent effect is included, the calculated 1H and 15N chemical shifts show remarkable improvement over those from the gas phase calculations, while the nonpolar 13C chemical shifts are less affected by the solvent. In addition, to accurately calculate the 1HN chemical shifts, the explicit solvent method should be taken into account. However, although the inclusion of solvent effect shows significant improvement for 15N chemical shifts, they still have large deviations from the experimental values.

Our study also demonstrated that the AF-QM/MM calculated result accurately reflects the dependence of 13Cα chemical shifts on the secondary structure of proteins, and the use of 1H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable as proton chemical shift is highly influenced by the local chemical environment. The use of ab initio calculated chemical shifts is capable of facilitating accurate protein structure refinement and determination.

The AF-QM/MM method can be further utilized to predict other local chemical properties, such as chemical shift tensor anisotropies and J coupling constants. The applications may also be extended to more general biological systems, such as proteins with nonstandard residues, metalloproteins, protein-ligand, protein-DNA/RNA and membrane protein-lipid complexes.