The NMR Chemical Shift: Local Geometry Effects - American Chemical

Chapter 16

The NMR Chemical Shift: Local Geometry Effects Angel C. de Dios, Jennifer L. Roach, and AnnE.Walling

Downloaded by AUBURN UNIV on April 18, 2017 | http://pubs.acs.org Publication Date: August 20, 1999 | doi: 10.1021/bk-1999-0732.ch016

Department of Chemistry, Georgetown University, 37th and Ο Streets, NW, Washington, D C 20057

The dependence of the principal components of the nuclear magnetic resonance (NMR) chemical shift tensor of non-hydrogen nuclei in model dipeptides is investigated. It is observed that the principal axis system of the chemical shift tensors of the carbonyl carbon and the amide nitrogen are intimately linked to the amide plane. On the other hand, there is no clear relationship between the alpha carbon chemical shift tensor and the molecular framework. However, the projection of this tensor on the C-H vector reveals interesting trends that one may use in peptide secondary structure determination. Effects of hydrogen bonding on the chemical shift tensor will also be discussed. The dependence of the chemical shift on ionic distance has also been studied in Rb halides and mixed halides. Lastly, the presence of motion can have dramatic effects on the observed NMR chemical shift tensor as illustrated by a nitrosyl meso-tetraphenyl porphinato cobalt (III) complex.

The N M R chemical shift, the most prevalent parameter in N M R spectroscopy, carries a wealth of information regarding the environment and the local electronic structure in the vicinity of the nucleus under study.(i). For example, one normally finds a different chemical shift for the C nucleus of each alanine residue in a protein. Ideally, a thorough analysis of the N M R chemical shift can yield information regarding the structure and interactions in the vicinity of the nucleus concerned. To achieve this, a detailed understanding of how geometrical factors and intermolecular interactions influence the chemical shift is crucial. The development and validation of the methods towards this end have combined powerful and efficient ab initio quantum mechanical techniques, which have been a

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© 1999 American Chemical Society

Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.


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extensively tested in small molecules, with a model for partitioning the contributions to the chemical shift in a system as complex as a protein and calculating each contribution as rigorously as possible. There are two strategies important in successfully predicting chemical shifts. First, it is necessary to determine the factor, i f there is one such factor, that is primarily responsible for the observed changes in chemical shift. This search becomes possible i f the chemical shift is categorized into various contributions; intra- and intermolecular effects. The distinction between intraand intermolecular effects is particularly useful in choosing an appropriate model fragment that has a size present computational capabilities can still address. Furthermore, with intramolecular factors, one can consider separately the dependence of the chemical shift on various geometrical parameters such as bond lengths, bond angles and dihedral angles. Categorization of the chemical shift into various contributions is exemplified in the rovibrational averaging of the N shielding in N H (2) and P in P H (3), following the pioneering work of Raynes and coworkers for the nuclei in H 0 (4) and C H (5). From the same group, the first categorization of intermolecular effects on the N M R chemical shift was also made (6). The second important strategy is choosing an appropriate model fragment. Even with present computational software and hardware, it is still necessary to limit the number of atoms in a calculation. Selecting the right model enables the use of large basis sets and higher levels of theory. In addition, a correct model should also make it possible to investigate separately the various contributions to the chemical shift. For example, seven years ago, it was not yet possible to perform shielding calculations for Xe. Using A r as the model, experimental Xe chemical shifts in the gas phase and as adsorbed species in zeolites were successfully reproduced using ab initio methods (7). The same methods that successfully reproduced observed chemical shift trends in small molecules have already been shown to be equally applicable to systems as complex as proteins where not only the large number of atoms impeded ab initio treatments, but the presence of several factors such as local structural (torsion angle, bond angle, and bond length) constraints, electrostatic interactions and hydrogen bonding served as additional challenges as well. Combining the above two strategies with the local origin methods; enhanced gauge-including atomic orbital (GIAO) method (8-9), individualized gauge for localized orbitals (IGLO) method (10), and the localized orbital local origin (LORG) method (77), led to the successful prediction of N M R chemical shifts in proteins via ab initio methods (72). Most of the ab initio studies of N M R chemical shifts in peptides and proteins have focused on the average or isotropic value of the N M R chemical shift. The chemical shift is a tensor quantity and is, therefore, capable of providing six independent pieces of information, namely, the magnitude and direction of each of the three principal components. In general, the shielding tensor can be antisymmetric, leading to nine independent components. However, only the symmetric part of the shielding tensor is relevant to the experiments 1 5

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222 described in this work. Thus, all references to components of the shielding tensor in the remainder of this paper will concern only the symmetric part of the tensor. Any ab initio package that calculates shielding provides at the same time the full shielding tensor information, hence, no computation in addition to those required for deriving the isotropic value is necessary to obtain the complete N M R chemical shift tensor. Several papers on novel solid-state N M R experiments that offer the possibility of obtaining shielding tensor information in peptides have been published recently (13-16). Designing experiments that will take advantage of all the information available from a shielding tensor is extremely challenging. Although the magnitudes of each of the principal components can be readily extracted from a powder spectrum, the determination of the orientation of the principal axis system of a shielding tensor normally would require single crystalline samples. Thus, it may not be experimentally feasible, for example, to determine how the orientation of a shielding tensor for a given site in a polypeptide changes with secondary structure. The adequacy of present shielding methodologies in predicting not only the magnitude but also the orientation of the principal components has already been demonstrated in the case of crystalline, zwitterionic L-threonine (17). Reasonable agreement is achieved for all the carbon sites, even in the presence of charged (COO-, R N H ) and polar groups (-OH). With this capability, it is now possible to probe theoretically the behavior of the shielding tensor, specifically, its orientation as a function of local structure and environment. Such information is impossible to obtain empirically. The shielding tensor can be influenced by either short-range or long-range factors. Unlike experiments, theoretical calculations can also focus on one factor at a time. For example, the effect of changing one of the dihedral angles can be studied separately. Hydrogen bonding can also be studied. Such studies may not be possible experimentally, especially when most of the factors are normally simultaneously changing from one system to another. Thus, theoretical work on chemical shielding tensors in peptides can be used to explore trends that may become useful in designing and verifying novel experiments which will fully utilize the information available from chemical shift measurements. +

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Chemical Shift Tensors in Peptides Details of this section have already been published (18). The model used in calculating amide Ν and C shielding tensors was an N-formyl-glycylglycine amide fragment. Hydrogen bonding was simulated by incorporating a formamide molecule. For the C shielding tensor, an alanyl-X-amide fragment was used where X is one of the naturally occurring amino acids. The shielding tensor is obtained using the deMon-NMR program (19). The spatial relationship of the shielding tensor of amide nitrogen sites in adjacent residues is governed by the dihedral angle ψ (see Figure 1). If the principal axis system (PAS) of the amide nitrogen shielding tensor follows the molecular framework then this spatial relationship becomes a simple function of ψ. Figure 2 displays a tensor plot for the shielding of the amide Ν site in an extended conformation. In this a



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Figure 1. Model peptide fragment showing the spatial relationship between Ν shielding tensors of adjacent residues and the dihedral angle ψ.

Figure 2. A tensor plot of the amide Ν shielding tensor for an extended conforma tion. (Reproduced with permission from ref. 18. Copyright 1997 American Chemi cal Society.)


224 figure, the tensor is represented by a Jorgensen-Salem plot (20) in which the distance of the contour from the nucleus under study (in this case, the amide Ν nucleus) in a given radial direction is proportional to the absolute shielding response to an external magnetic field applied in that direction. At this conformation, the least shielded component is tilted by about 19° from the N - H bond while σ lies normal to the amide plane. The σ component is very close to being perpendicular to the C'-N bond (as a result of its partial double bond character) while σ lies almost parallel to this bond. Sampling the entire Ramachandran surface (a surface describing the shielding at various φ and ψ values, where -180° < φ < 180° and -180° < ψ < 180°), it is found that only the least shielded component, σ , stays related to the molecular framework. In all conformations, this component lies on the amide plane and is tilted by about 18° 22° from the N - H vector (or nearly perpendicular to the C ' - N bond). The calculated magnitude and orientation of the principal components in the extended conformation are in quantitative agreement with values observed experimentally (16, 21). From this theoretical work, it is also observed that the other components, σ and σ , do not strictly follow the amide plane. In fact, in the helical region, σ is no longer normal to the amide plane for glycine residues. Only in extended and sheet dihedral angles does one component appear to be normal to the amide plane. One can, however, still take advantage of the fact that the least shielded component is following the N - H vector. In the presence of hydrogen bonding as represented by a formamide molecule in the calculation, the isotropic shielding goes down by 4-5 ppm. The behavior of each principal component is dependent, however, on secondary structure. For extended and helical conformers, only σ and σ are significantly affected by hydrogen bonding. For sheet-like geometries, all three components are sensitive to hydrogen bonding, with σ showing a dependence of opposite sign. Since the overall effect of hydrogen bonding on the isotropic shielding is invariant with secondary structure, σ and σ become even more sensitive to hydrogen bonding in sheet-like conformers. Finally, hydrogen bonding does not have any significant influence in the direction of the principal components. Figure 3 displays a tensor plot for the C shielding in the extended conformation. Using a glycyl-glycine fragment and sampling the whole Ramachandran surface, the C shielding tensor is found to follow the molecular framework. The spatial relationship between the shielding tensors of C sites in adjacent residues is hence a simple function of the dihedral angle φ. The principal tensor element σ (which has a value close to that of a bare C nucleus) always lies close to the C=0 bond (7° - 9°). The most shielded component always lies normal to the amide plane while σ lies on the amide plane and is perpendicular to the C=0 vector. Clearly, a 2D solid-state N M R experiment that correlates two C shielding tensors, as in the experiment proposed by Weliky et al. (75), is certainly ideal. Inclusion of hydrogen bonding results in deshielding. The component most sensitive to hydrogen bonding is σ when a linear hydrogen bond is assumed for Ο H - N and a 120° angle for C=0 H . In addition, it is also 22

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Figure 3. A tensor plot of the C shielding tensor for an extended conformation. (Reproduced with permission from ref. 18. Copyright 1997 American Chemical So ciety.).


226 observed that helical models are more sensitive to hydrogen bonding which perhaps explain why C sites in helical residues are generally more deshielded compared to those in sheet regions of a protein. As in the amide N , the orientation of the principal components is also not affected by hydrogen bonding. Of all sites in a protein, the shielding of the C nucleus seems to be the most tractable, being dependent only on the torsion angles φ, ψ and χ. Even for this site, however, the error is still within 1 ppm, which translates to about 10% of the largest observed chemical shift range for C in proteins for any given amino acid. Therefore, it would be useful to find a more sensitive piece of the chemical shift tensor that may have the same amount of error but a greater sensitivity to the secondary structure of the protein. The value of the shielding tensor along the C - H bond is a possible candidate. The isotropic chemical shift of helical C sites is found to be deshielded compared with those of sheet geometry (12, 22). Surprisingly, an opposite trend is seen when one looks at the projection of the C shielding tensor on the C - H bond. With sheet dihedral angles (φ = -120°, ψ = 120°), the least shielded component almost lies parallel to the C - H vector. On the other hand, with a helical conformation (φ = -60°, ψ = 60°), the contribution of the least shielded component to the projection of the C shielding tensor on the C - H bond becomes minimal. Although the difference between the isotropic chemical shifts of helical and sheet C is about 5-8 ppm, the difference between the projection of the C shielding on the C - H vector can be as large as 22 ppm. These differences become more evident when one compares the tensor plots of the C shielding in sheet and helical geometries as shown in Figure 4. In the sheet geometry (Figure 4A, φ = -120°, ψ = 120°), it can be seen that the short axis (most deshielded) of the shielding tensor coincides with the C - H bond, while for a helical residue (Figure 4B, φ = -60°, ψ = -60°), this is no longer true. This exciting trend has already been observed and verified in 2D and 3D solution N M R experiments (23). a

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ELECTROSTATIC EFFECTS

There is considerable interest in measuring and interpreting the influence of electric fields on N M R chemical shifts. In real systems, the perturbing electric field can be attributed to the presence of nearby molecules or charged groups. A sound interpretation of how and why chemical shifts change with environment should lead to a better understanding of the intermolecular interactions that give rise to such perturbations. Several simplified strategies addressing the effects of long-range interactions on the N M R chemical shift are now available (24 and references therein). Carbonmonoxy heme proteins offer an excellent testing ground for theories regarding the effects of weak intermolecular interactions on the N M R chemical shift. Park et al. (25) first noted interesting correlations between various electronic properties such as vibrational frequencies, chemical shifts and quadrupole coupling constants in various carbonmonoxy heme proteins. In this series of proteins, they established a linear relationship between the C and 0 1 3


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Figure 4. (A) A tensor plot of the C* shielding in alanine with sheet dihedral angles (φ = -120°, ψ = 120°). (Β) same as (A), but with helical dihedral angles (φ = -60°, ψ = -60°). (Reproduced with permission from ref. 18. Copyright 1997 American Chemical Society.)


228 N M R chemical shifts, and the CO vibrational stretching frequencies. Augspurger et al. (26) later proposed a model for these observed correlations. And in their work, the computed relationships bear the same sign as the experiment although the magnitudes seem overestimated. Using a model (see Figure 5A) consisting of Fe octahedrally coordinated to five negative point charges (each one has a charge of -0.4e) and a C O molecule, the effects of uniform and non-uniform electric fields applied along the Fe-C-0 axis on the chemical shifts of C and 0 and the C O stretching frequency have been reinvestigated (27). The correlations (as described by the slope of a linear curve relating the chemical shifts to the CO stretching frequency) obtained from this model are; C , -0.11 ppm/cm" and 0 , 0.28 ppm/cm" (Figure 5B), to be compared with the experimental values (Figure 5C); -0.07 ppm/cm" and 0.26 ppm/cm" , respectively. These calculated values were all obtained using a linear Fe-C-0 geometry. This study has already been followed by a more exhaustive experimental and theoretical work supporting the fact that C O binds to Fe in a close to a linear arrangement in all conformational substates of carbonmonoxy heme proteins and model compounds (28). Weak electrical perturbation acting as the main factor appears to be responsible for all the observed relationships. The presence of factors other than weak electrical perturbation will not lead to such correlations between so many spectroscopic parameters. The success of the model used in this work (27) illustrates the adequacy of present shielding computational methodologies in extracting intermolecular effects on chemical shifts. 2+

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Hydrogen Bonding One factor that can significantly affect the magnitude of the isotropic shielding and its principal components (as seen in amide Ν and carbonyl C sites) is hydrogen bonding. To study this factor in detail, theoretical and experimental N N M R studies are ongoing (Wei, Y.; McDermott, A ; Roach, J. L.; de Dios, A . C , unpublished data), in collaboration with McDermott at Columbia University. Specifically, the shielding tensor of one of the imidazole ring nitrogens (see Figure 6) is studied as a function of hydrogen bond distance. Shown in this figure is the calculated orientation of the PAS of the N shielding tensor. The most shielded component is normal to the plane of the molecule while the least shielded component lies parallel to the N - H bond. The hydrogen bond partner used in the calculations is an acetate ion. A series of small histidine containing compounds (ranging from L-His through small peptides (2 - 3 residues)) which have known high-resolution structures (the hydrogen bond distance is known within 0.01 Â) is being investigated. Preliminary experimental results show that the isotropic N N M R chemical shift changes by about 13 ppm as the hydrogen bond distance changes from 2.60 to 2.85 À. This change is primarily due to changes in one of the components, σ . Theoretical studies which make use of a protonated imidazole molecule hydrogen bonded to an acetate ion are in agreement with experiment. In Figure 7, the measured values of the principal components of the N shielding tensor are plotted against the hydrogen bond 1 5

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Figure 5. (A) Model fragment used in shielding and frequency calculations for [FeCO] . (B) Calculated correlations between C and 0 N M R chemical shifts and CO stretching frequency. (C) as in (B), but with experimental values (26). ((B) Reproduced with permission from ref. 27. Copyright 1997 American Chemical Society. (C) Adapted from ref. 26.) 2+

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Figure 6. Model fragment used in N shielding calculation for imidazole. Also shown is the calculated orientation of the principal axis system of the shielding tensor. (Adapted from reference 26. Copyright 1991 American Chemical Society.)



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Figure 7. Experimental (•) and calculated (linear curve) N shieldings for imidaz ole. (Α) σ . (Β) σ . (c) σ . (D)

The NMR Chemical Shift: Local Geometry Effects - American Chemical

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