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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Phys Chem B. Author manuscript; available in PMC 2014 January 24.
Published in final edited form as:
PMCID: PMC3564578

Quantum Chemical Calculations of Amide-15N Chemical Shift Anisotropy Tensors for a Membrane-Bound Cytochrome b5


There is considerable interest in determining amide-15N 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-15N CSA tensor have been determined using density functional theory for a 16.7-kDa membrane-bound paramagnetic heme containing protein, cytochrome b5 (cytb5). All the calculations were performed by taking residues within 5Å distance from the backbone amide-15N nucleus of interest. The calculated amide-15N CSA spans agree less well with our solution NMR data determined for an effective internuclear distance rN-H = 1.023 Å and a constant angle β = 18° that the least shielded component (δ11) makes with the N-H bond. The variation of amide-15N 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.


NMR has become an obvious choice to study the structure and dynamics of ground and excited states of biomolecules in solution and solid-state.14 While increasing number of atomic-level 3D structures of proteins are commonly solved using multidimensional NMR spectroscopy, recent studies have demonstrated the importance of the very basic NMR parameter – chemical shift – for high-throughput structural studies.57 In addition, chemical shift tensor that reveals the local electronic environment surrounding nucleus8 has emerged as one of the most important module that is widely used for better interpretation of structure57, 913 and dynamics1418 of biomolecules. CSAs are in fact essential to study aligned samples such as proteins and peptides embedded in lipid bilayers or bicelles using solid-state NMR spectroscopy.19 Although previous studies have shown that CSA tensors can be measured directly from well-behaved water-soluble proteins, extension to membrane proteins remains a major challenge.2023 In fact, structural studies of membrane proteins using solid-state NMR techniques heavily rely on the CSA tensors determined from model peptides. However, the CSA tensors of a given nucleus can depend on the nature of the environment. For example, 15N chemical shift highly depends on the electrostatic interaction.24, 25 Therefore, there is considerable interest in determining CSA parameters directly from membrane-bound proteins. To this end, in this study, we report amide-15N CSA tensors from a membrane-bound cytochrome-b5 (cytb5) determined using quantum chemical calculations and compare them with CSA values determined from experimental measurements to understand their variation in detail. Because of the above-mentioned importance of the chemical shift parameters, a plethora of studies focused on the development of approaches to measure them accurately. Computer programs have been developed to accurately predict chemical shift tensors for biomolecules,11, 2629 which are increasingly used to determine their secondary and tertiary structures.5, 9, 3032 A number of experimental methods have been developed for the determination of anisotropic component of the chemical shift tensor both in solids and solution. Due to fast change in the orientation of molecules in solution, the anisotropic interactions are averaged out resulting in a lack of information about individual components of chemical shift anisotropy (CSA) tensors from the frequency of NMR peaks. Relaxation experiments are mostly used for the determination of CSA tensors from solution NMR studies.18, 20, 22, 23, 3336 In solids, where the motion of the molecules is restricted, CSA tensors can be determined by several methods such as static NMR measurements from single crystals,37, 38 static powder pattern,3942 magic angle spinning,4348 two-dimensional separated-local-field (SLF) experiments49, 50 and recoupling methods51, 52 from polycrystalline sample. However, a study on the variation of CSA tensors obtained through NMR experiments alone is not sufficient to completely characterize a system, it requires the use of quantum chemical calculations as an alternative. The accurate and precise determination of CSA tensors is essential for better interpretation of experimental results. Recent advancements in high performance computing resources have enabled efficient and accurate chemical shift tensor calculations for a variety of biomolecules. Quantum chemical calculations using semiemperical, ab initio Hartree-Fock theory or density functional theory (DFT) have been routinely used for the determination of chemical shift tensors8, 5365 in a range of compounds and the accuracy of the outcome is exclusively dependent on the level of theory used.6670

Automated fragmentation quantum mechanics combined with molecular mechanics (AF-QM/MM) is also being used for precise determination of isotropic as well as anisotropic components of chemical shift tensors from biomolecules.7174 Reports on amide-15N CSA tensors for large biomolecules are relatively less in comparison to 1H and 13C CSA as they are very sensitive to backbone torsion angles/secondary structure, amino acid sequence, inter and intra molecular hydrogen bonding interactions, intra-residue angle, chemical nature of side chain, electrostatic interactions and solvent effect.60, 61, 7580 Hence, their determination with higher accuracy and precision becomes a daunting task. Many attempts have been made in past for the determination of both isotropic as well anisotropic components of amide-15N chemical shifts of biomolecules using quantum chemical calculation.25, 54, 81, 82 A theoretical study by Poon et al.,24 provided a methodical analysis of how the amide-15N CSA tensors vary in different peptides. Several computational methods were developed by Cai et al.,83 that included most of the important effects influencing amide-15N CSA values for helical residues of protein G. In another study, a disagreement of computed principal components of 15N CSA tensors with experimental data in beta-sheet and turn residues of protein G was assessed.84 In a recent work AF-QM/MM method was used for the computation of CSA tensors where the variation of the anisotropies matched well with solid-state NMR results in comparison to solution NMR measurements.73


In this study, quantum chemical calculations of backbone amide-15N chemical shift tensors for cytb5 were performed using Gaussian 0385 program. Gauge-including atomic orbital (GIAO) method8689 in combination with density functional theory using Becke-Lee-Yang-Parr (B3LYP) exchange-correlation functional was employed.90 In the calculations, a higher basis function 6-311+G(2d,p) and a relatively lower basis function 6-31G(d,p) basis function91 were used for nitrogens and all other remaining atoms, respectively, to reduce the computational time. The atomic coordinates were taken directly from the NMR structure of membrane-bound cytb5 without any further optimization.92 The cytb5 structure incorporated in membrane employed in our calculation was derived from CYANA93 using constraints obtained from NOESY and backbone assignment data.92 This was followed by HADDOCK (High Ambiguity Driven biomolecular DOCKing)94, 95 simulations to dock the heme in the NMR structure of cytb5 calculated using CYANA. The distance restraints for docking heme were essentially taken from previously reported cytb5 structure (PDB code 1DO9)96 where pseudocontact shifts were employed as one of the constraints for solving the structure of ferric microsomal rabbit cytb5. Details of the structure of full-length membrane-bound ferric cytb5 will be reported elsewhere. A previous quantum chemical calculation study on short peptides showed that amide-15N CSA can be accurately determined by considering all atoms and charges within about 5Å distance from the 15N of interest.24 Similarly, the calculations in the present study were performed by taking all the residues of cytb5 within a 5Å distance from the atom of interest (amide-15N). Chemical shielding constants obtained from calculations were converted to chemical shift frequency values by calculating the difference from the isotropic chemical shift value of liquid ammonia (δ = 244.6 ppm at 25°C) using the relation,97 δii = 244.6 - σii. Here, δii and σii represent the principal components of the chemical shift tensor and the chemical shielding constant in ppm, respectively. The three principal components of the chemical shift tensor follow the usual convention δ11 ≥ δ22 ≥ δ33.


Cytb5 is a 16.7-kDa (134 amino acid residues) electron transfer protein present in eukaryotic organisms. It contains a water-soluble domain (M1-K91) with a paramagnetic heme unit in the N-terminal region, a transmembrane helical domain (S105-L125) in the C-terminal region, and an unstructured 14-residue long linker region (L92-D104) which connects the transmembrane and soluble domains.98, 99 The different structural elements of the membrane-bound cytb5 along with its amino acid sequence are shown in Figure 1.

Figure 1
Structure of different regions along with amino acid sequence of a membrane-bound protein cytochrome-b5

In a recent study fragment based calculations using adjustable density matrix assembler (ADMA) approach was implemented for the prediction of isotropic chemical shifts to a higher accuracy based on the level of theory, proper selection of basis set used and the size of the molecular fragment considered for the calculation.57 Other studies27, 83 recommended the inclusion of 7–9 residues in the calculation for residues in an alpha-helix, which is to avoid terminal artifacts due to a lack of interacting H-bonded partners and a change in the dipole moment of the helix. Therefore, to calculate accurate amide-15N chemical shift tensor values and to keep the computational time at an optimum, in this study we have carried out calculations by considering at least 5–6 residues on either side of the 15N nucleus of interest, in addition to including all residues present within 5 Å distance from the 15N atom, irrespective of the secondary structure (whether it belongs to alpha-helix, beta-sheet or turn). Representative regions surrounding a few selected residues (D36, E48, H44 and M96) of cytb5 used in the calculations are shown in Figure 2. Since none of the residues of the soluble domain are located within 5 Å distance from the linker region residues, the amide-15N CSA calculations were performed by taking the complete linker region along with the end residues from the soluble domain of the protein in order to avoid any terminal artifacts as shown in Figure 2.

Figure 2
Representations of atoms within 5Å distance from a few selected residues (D36, E48, H44 and M96) of cytb5 included in the quantum chemical calculation of amide-15N CSA using Gaussian-03.

Comparison of calculated and experimental backbone amide-15N isotropic chemical shift values of cytb5

Amide-15N isotropic chemical shift values of amino acid residues of cytb5 were calculated from the computational method as described above. The calculated values are compared with the experimentally determined values in Figure 3A; refer to Table S1 in the Supporting Information for the chemical shift values. The range of calculated isotropic chemical shift values is slightly larger (102.7–134.3 ppm) than the range of experimentally determined values (105.3–130.8 ppm),35 which is still smaller than the range reported for Tfb1/p53 complex in a recent work.56 Interestingly, in another report57 it was shown that the use of 6-311g(d) basis set coupled with B3LYP functional produced larger deviations in comparison to experimental results. However, in the present study, the use of larger basis set 6-311+g(2d,p) on 15N is shown to reduce the variation when compared to the experimental data. This result shows that the addition of diffused and polarized functions in the calculation could improve the agreement between calculated and experimental data. It is worth mentioning that although the use of a larger basis set leads to a better agreement with experimental data, the required computational time was found to be longer.

Figure 3
Amide-15N isotropic chemical shifts of cytochrome-b5

The difference between the calculated and experimental chemical shift values lies within a range of ±15 ppm (Figure 3B). In fact, for most residues, the difference is less than ±10 ppm, which is similar to discrepancies reported from other computational studies on globular proteins in the literature.72, 84 The calculation performed in this study was in gas phase and does not include any solvent effects and motional averaging. The omission of these effects in the calculation could contribute to the observed discrepancies between calculated and experimental chemical shift values obtained from solution NMR measurements.56, 68, 69, 74, 100102 In a previous study a difference of ~5 ppm in experimentally measured isotropic chemical shift values was reported between oxidized and reduced state of cytb5.103 Therefore, the interaction of amide nitrogen with the paramagnetic center of the heme unit could also contribute to the discrepancy. One of the possible reasons for a large difference of ~9–15 ppm between calculated and experimental chemical shift values for V50, E53, Q54, A55, G56, D58, A59, T60 and N62 (circled residues in Figure 3B) located in close proximity to the heme unit of cytb5 could also be due to this interaction. We thought the inclusion of the heme unit in the calculation could further improve the agreement between calculated and experimental values as the interaction of amide nitrogen with paramagnetic center is now taken into account. However, even the inclusion of the heme unit in calculations for V50, E53, Q54 and N62, as it lies within 5Å distance from amide-15N of interest, did not improve the agreement between calculated and experimental data. This suggests that the interaction of amide nitrogens of these residues with the low-spin paramagnetic center (Fe (III)) of the heme unit is not fully taken into account in our calculations possibly due to limitations of the DFT method used for the metal ion. It is also possible that the interaction between the paramagnetic center and amide nitrogens could extend beyond the 5Å distance from the 15N of interest. Longer computational time requirement prevented further calculations using a higher basis function on the metal ion along with the inclusion of large number of atoms.

Variation of calculated principal components with the inclusion of atoms beyond 5Å distance from amide-15N

Previous studies have shown that the calculated 15N CSA values highly depend on the size of the molecular portion considered in the calculation.24, 27 Portions of the molecule considered for calculations in this study are depicted in Figure 2. To examine the accuracy of CSA values calculated by taking residues within 5Å distance from the chosen residue, we also carried out calculations by taking residues within 4Å and 6Å distances for a few selected residues (K19, T60, N62, E64 and D71) of cytb5. The calculated values for these residues are plotted in Figure 4 and also listed in Table S1 in the Supporting Information along with their isotropic chemical shift constant, CSA values and span. It can be seen from Figure 4 that the variations in the calculated δ11, δ22 and δ33 values are small when the distance is changed from 4 Å to 5 Å and become constant afterwards; an exception of residue N62 that shows slightly a higher variation for δ22 and δ33 in comparison to other residues at a larger distance. However, this variation can be significant for residues close to heme depending on the inclusion of heme in the calculation. We chose the residue D71 to demonstrate this point. The heme unit was absent when we considered residues within 4Å distance from D71 while it was present when 5Å or a larger distance was used. Calculated values for the least (δ11) and most (δ33) shielded components are decreased by ~8.5 and ~5.0 ppm, respectively, with ~7.0 ppm change in the CSA span. This variation could be attributed to the ring current effect from the aromatic porphyrin ring of the heme unit. Calculations were also performed for N62 and D71 by considering residues within a distance of 8Å (refer to Table S1 in the Supporting Information for amide-15N CSA values). A substantial change in δ33 value was observed when increasing the distance from 6 to 8Å for these residues. It should be mentioned that the increase in the radius from 6Å to 8Å obviously increased the number of atoms included in the calculation; this was computationally demanding and it might have contributed errors in the calculation due to a superposition of extensive number of mixed basis sets used in the calculation.

Figure 4
Variation of principal components of CSA tensor with the size of molecular fragment considered in the calculation

Variation of principal components of amide-15N CSA with isotropic chemical shift

The variation of the principal component values with the isotropic chemical shift (δiso) values is represented in Figure 5. The best-fit lines correspond to δ11 =1.43δiso + 55.25, δ22 = 0.41δiso + 35.20 and δ33 = 1.16δiso - 90.45 and are shown in Figure 5A. It is evident from Figure 5A that the least (δ11) and the most shielded (δ33) components of the amide-15N CSA tensor vary significantly while δ22 shows a minor variation when plotted against the isotropic chemical shift.

Figure 5
Principal components of amide-15N CSA tensor vs isotropic chemical shift

Nitrogen-15 CSA were experimentally determined under the assumption of an axially symmetric tensor i.e., δ22 = δ33. Therefore, to compare the variation of principal component values obtained from calculations with the experimentally determined values (refer to Figure 5C), an average (δave) of δ22 and δ33 were plotted along with δ11 against the isotropic chemical shift in Figure 5B. The two best-fitted lines having linear correlations with the isotropic chemical shift correspond to δ11 = 1.43δiso + 55.25 and δave = 0.78δiso - 27.63 (Figure 5B), while the experimental best-fitted lines have linear correlations as δ11 = 1.29δiso + 81.55 and δ22 = δ33 = 0.85δiso - 40.77 (Figure 5C). The slope values reported in Figure 5 suggest that the variations of the calculated (Figure 5B) and experimental (Figure 5C) principal component values with the increasing isotropic chemical shift are nearly similar. However, it is important to note here that the computationally obtained principal components show a narrow distribution (Figure 5B) as compared to the experimentally determined values (Figure 5C). One of the possible reasons for a large spread of 15N CSA components determined from CSA-dipolar cross-relaxation experiments using solution NMR method have been ascribed to the inclusion of a correction due to the effects of rapid internal motion.104, 105 These effects were not included in our calculations in the present study; whereas we expect that inclusion of these effects could result in a better agreement with experimentally measured principal components of amide-15N CSA.

Variation of principal components of amide-15N CSA tensors in secondary structural elements of cytb5

The average value of calculated backbone amide-15N CSA defined as Δδ = δ11 – 0.5 × (δ2233) for cytb5, 162.2 ppm, is slightly less than the experimental value of 171.7 ppm.35 Nevertheless, these values fall within the range of amide-15N CSA values previously reported for biomolecules from solid-state NMR, solution NMR and quantum chemical studies.16, 2022, 33, 39, 40, 53, 82, 84, 106114 The backbone amide-15N CSA is sensitive to various factors such as intramolecular hydrogen bonding and side chain chemistry. As a result 15N CSAs of residues located in different structural elements of the protein can show a variation. In order to understand the amide-15N CSA dependence on the secondary structure of the protein, we calculated amide-15N CSAs for residues in alpha helices, beta sheets and turns of cytb5. The mean 15N CSA value is found to be similar for residues in the alpha-helix (165.2 ppm) and the beta-sheet (165.4 ppm) while it is smaller (156.5 ppm) in the turn regions. Lower mean 15N CSA value for residues in turns can be attributed to the flexibility due to lack of H-bonding interactions. The observed trend in this study is similar to an earlier report on protein G from density functional calculations84, while CSA measurements on GB3, cytb5 from solution NMR35, 115 and GB1 from solid-state NMR47 experiments showed higher mean amide-15N CSA values for residues in alpha-helix in comparison to beta-sheet residues.

The dependence of principal components of the CSA tensor on the secondary structure of the protein can be evaluated based on their average values obtained from calculations. Average values of δ11, δ22 and δ33 are 231.4, 81.2, 51.3 ppm for residues in alpha helices, 232.8, 88.0, 47.7 ppm for residues in beta sheets and 224.4, 85.1, 50.7 ppm for residues in a turn, respectively. The turn residues are more shielded (~5–6 ppm) along the Z-direction (or along the direction of the least shielded component) of the chemical shift tensor in comparison to helical and beta-sheet residues. The least shielded component δ11 is very close to the direction of the hydrogen bond (N-H---O=C) in alpha-helix and beta-sheet25 and therefore it is more deshielded than that determined for the turn residues which lack such H-bonds. A substantial deviation from the axial symmetry, defined by asymmetry parameter, η = (δ22 - δ33)/(δ11 - δiso) was found for the secondary structure elements of cytb5. This value is found to be slightly smaller (0.28) for helical residues than that for the beta sheet (0.35) and turn (0.33) residues which fall within the range reported in the literature.7, 82, 115

The individual principal components of the calculated amide-15N CSA tensor for alpha-helix and beta-sheet residues of cytb5 were compared with experimental data obtained from solution NMR experiments (Table S3 in the Supporting Information). It is evident from Figure 6 that the principal components of amide-15N CSA tensor for alpha-helix and beta-sheet residues are in good agreement with the experimental values with a correlation coefficient of 0.98. The correlation lines have slopes of 1.14±0.03 and 1.01±0.04 for alpha-helix and beta-sheet residues, respectively. These results are in accord with reported values in the literature.84

Figure 6
Linear regression plots between the calculated principal components of amide-15N CSA tensors and the corresponding experimental components for alpha-helix and sheet residues

Variation of backbone amide-15N CSA tensors in individual alpha helices and beta sheets of cytb5

Amide-15N CSA values for residues in different alpha helices and beta sheets of cytb5 were calculated as explained earlier and the results are shown in Figure 7. The trend of CSA variation is almost similar for residues located in alpha helices (Figure 7A). Similarly, residues in beta-sheet conformation also have a definite trend of amide-15N CSA variation (Figure 7B). The β1/β5 and β2/β4 arranged in parallel to each other have opposite trend with a large variation while β3 which is flanked between β2 and β5 shows a narrow variation of amide-15N CSA. This uniform trend of variation of backbone amide-15N CSA suggests a uniform characteristic of the 15N nuclei in amide backbone of alpha helices and beta sheets wherein the residues are experiencing direct and indirect H-bonding interactions and also validates the CSA dependence on the backbone torsion angles. The calculated mean values of amide-15N CSA in individual beta-sheet show a significant variation (152.0, 171.2, 167.6, 168.5, 165.8 ppm for β1, β2, β3, β4 and β5, respectively) in contrast to values in individual alpha helices (166.7, 166.4, 163.9 and 167.0 ppm for four alpha helices shown in Figure 7A). This observation is in agreement with an earlier DFT report on protein G.84 The observed behavior may be because of H-bonding patterns in individual alpha helices and beta sheets. Residues belonging to the same helix (or residues adjacent to each other) participate in H-bonding whereas in a beta-sheet residues of different strands participate in H-bonding. This results in far more extended beta-sheet conformations in comparison to alpha-helix conformations; as a consequence residues in a beta-sheet are also dependent on the conformations of the other strand and therefore show larger variations in the calculated mean values of amide-15N CSA. It is also important to note that the variation for alpha-helix residues increases with a decreasing distance of the 15N of interest from the heme unit as shown in Figure 7A. Residues belonging to the first alpha-helix (L14-H20) are at a larger distance from heme and hence show a narrow distribution of CSA. The residues belonging to second (E48-Q54), third (T60-D65) and fourth (T70-F79) helices are located either above or below the plane of heme; as a consequence, the orientation of these residues must be a function of the position of the plane of the heme unit and therefore could result in a larger distribution of CSA as shown in Figure 7A.

Figure 7
Variation of backbone amide-15N CSA for different alpha-helix and beta sheet residues

Comparison of experimental and calculated spans of amide-15N CSA

The calculated CSA span which represents the difference between least shielded and most shielded components of CSA tensor given by the relation Ω = δ11 - δ33 (Table S2 in the Supporting Information) is compared with experimentally determined CSA span for values cytb5.35 The experimental CSA spans for backbone amide residues were obtained by assuming axially symmetric CSA tensors and considering an effective internuclear distance rN-H = 1.023 Å and a constant angle (β = 18°) between δ11 and the N-H bond. As shown in Figure 8A, the variation in the calculated spans is smaller than the experimentally measured span values. One of the recent reports using an automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method for 15N CSA determination from water-soluble GB1 and GB3 proteins also validates this aspect.73 15N CSA obtained from solution NMR studies were found to show a larger variability as compared to solid-state and quantum mechanical/molecular mechanical calculations. This is attributed to the fact that the solution NMR approach applies a correction for the effects of small amplitude internal motion which can alter N-H bond length (by ~ 10–15%),21, 106, 116, 117 while solid-state NMR utilizes the motionally averaged CSA and N-H dipolar couplings.33 In addition, the use of fixed values for the N-H distance and angle β could contribute to the variations of 15N CSA obtained from a solution NMR study. It was also experimentally observed that the residues near the heme unit of cytb5 exhibited a slightly larger variation in the amide-15N CSA span as compared to earlier reports on water-soluble proteins. To understand the variation more closely through quantum chemical calculations we carried out an investigation based on the calculated CSA span for the residues near heme. An expanded region of Figure 8A depicting residues near the heme unit (residues 39 to 79) is shown in Figure 8B. It can be seen that the trend in the variation of calculated amide-15N CSA span for these residues is almost similar to our experimental data with few exceptions. Calculated amide-15N CSA span for residues near the heme unit such as F40, L41, E42, E43, H44, L51, R52, E53, Q54, A55, A59, E61, F63, E64, H68, T70, E74, S76, T78 and F79 show a difference in amide-15N CSA span greater than 15 ppm when compared to experimental data. Out of these residues the calculations were performed only for H44, L51, E53, Q54, A59, F63, H68, A72, R73, S76 and F79 with the inclusion of the heme unit as it lies within 5Å distance from these residues. It is clear that the inclusion of the heme unit in the calculation didn’t improve the comparison with the experimental data, which could be due to the limitation of the level of theory applied in the DFT calculations as explained earlier.

Figure 8
A comparison of experimental and theoretical backbone amide-15N CSA spans determined from solution NMR and Gaussian calculations


In summary, we have determined backbone amide-15N CSA tensors for a heme-containing membrane-bound protein, cytb5, using DFT calculations. We believe that these CSA parameters can be utilized in the structural and dynamic studies of proteins using solid-state and solution NMR techniques; there is no need to rely on the CSA tensors determined from model peptides. The calculated CSA provides further insight into the experimentally measured CSA values. The variation in computed CSA shows a narrow distribution as compared to the experimentally measured data. However, the overall trend in the variation of CSA spans obtained by the two different approaches is in close agreement for most regions of the protein. It is important to note here that the calculations were performed on a rigid single molecule in gas phase that did not include motional averaging, rapid fluctuations of NH bond length and solvent effects. Omission of these effects could also result in discrepancies in the outcome and hence it becomes vital to incorporate these effects in calculation in the future studies. Our results suggest that the effect of the paramagnetic center is not fully taken into account possibly due to the limitation of theory employed in this study to avoid a long computational time. However, it is worthwhile to determine the effect of the metal ion in such paramagnetic systems to improve the accuracy of the calculated CSA values. It is of great importance to perform such calculations and solution or solid-state NMR experiments to determine CSA tensors from intrinsic membrane proteins such as G-protein coupled receptors. Such studies would enable the use of CSAs – instead of isotropic chemical shifts – to study protein-protein and protein-ligand interactions, which will provide insights into the function of the protein and could aid in the design of drugs/compounds to alter the function of the protein.

Supplementary Material



We would like to thank the CAEN Advanced Computing (CAC) facility at the University of Michigan for providing the computer resources to carry out the DFT calculations. This research is supported by funds from NIH (GM084018 and GM095640 to A.R.).


Supporting Information

Tables for the calculated values of the principal components of amide-15N CSA tensors for few residues of cytb5 with distance from backbone amide-15N of interest; Backbone amide-15N CSA principal components for various residues of cytb5 determined from quantum chemical calculations within 5Å distance from residue of interest; Parallel (δ, ppm) and perpendicular (δ[perpendicular], ppm) components of experimentally measured amide-15N CSA for alpha-helix and beta-sheet residues of cytb5. This material is available free of charge via the Internet at


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