Derivation of 13 C chemical shift surfaces for the anomeric carbons of polysaccharides using ab initio methodology

Transcription

1 Derivation of 13 C chemical shift surfaces for the anomeric carbons of polysaccharides using ab initio methodology Guillermo Moyna and Randy J. Zauhar Department of Chemistry and Biochemistry, University of the Sciences in Philadelphia, 600 South 43 rd Street, Philadelphia, PA Poster presented at the 219 th ACS National Meeting, August 1999

2 Introduction NMR is perhaps the most useful technique in the study of macromolecular conformation and dynamics in solution. The general methods are well established and used routinely in structural studies of proteins, DNA, and polysaccharides. 1 Recently, the use of NMR data other than NEs and coupling constants in structure refinement, such as residual dipolar couplings and chemical shifts, is being investigated. 2,3 1 H and 13 C chemical shifts have been employed in refinement of protein and peptide structures using either empirical or theoretical relationships. 3,4 While the former methods are based on the parametrization of known physical relationships against large databases of chemical shifts for a particular type of compounds, the latter rely on the fact that accurate estimations of chemical shifts can be made from molecular conformation through ab initio calculations. 5 The work of ldfield and de Dios on the dependence of the Cα and Cβ chemical shifts with the protein,, and χ dihedral angles is exemplary, and has opened new avenues for the use of 13 C chemical shift in protein structure refinement. 6-8 In this poster we present an ab initio theoretical study on the variation of the 13 C chemical shift of the anomeric carbons as a function of the <,> dihedral

3 angles of the glycosidic bond in polysaccharide and glycopeptide model compounds. ur work greatly extends previous exploratory calculations performed on glycosidic bond models carried out by Wilson and Webb, Mazeau, and others We describe the determination of <,> shielding surfaces for (1 1), (1 2), (1 3), and (1 4) D-Glcp-D-Glcp model disaccharides in both the α and β configurations (Figure 1). The calculations were done with the 3-21G basis set, and scaled to reference results from 6-311G** level calculations. Similar surfaces were obtained for GlcNAc-1 Thr and GlcNAc-1 Ser using different configurations for the peptide moiety, and results obtained for both families of model compounds are compared. We also present the determination of periodic formulae of the form δ( 13 C) = ƒ(,) obtained by fitting the theoretical results to trigonometric series expansions suitable for use in molecular modeling simulations. ur investigations show the applicability of chemical shift surfaces to the study of conformational preferences of polysaccharides and glycopeptides in cases were other NMR data is unavailable.

4 Methods Input Structures. Model disaccharide and glycopeptide structures were built with Sybyl 6.5 (Tripos, Inc.). In order to generate the chemical shift surfaces as a function of the glycosidic bond conformation, a grid with o intervals in the o range for and was constructed, to give a total of 324 input structures for each model disaccharide. For each structure in the grid, the and dihedrals were held constant and the rest of the molecule fully optimized (AM1 semiempirical, Spartan 5.01), resulting in an adiabatic energy surface for each model molecule. The resulting structures were employed in 13 C chemical shift estimations. Isotropic 13 C Chemical Shift Calculation. The GIA (Gauge Independent Atomic rbital) method of Pulay and coworkers was used, as implemented in Gaussian Due to the computational expense of calculations at the 6-311G** theory level, shift surfaces were computed using the 3-21G basis set, and scaled to results from reference 6-311G** level calculations for selected 13 C saccharide resonances. In order to obtain the scaling factor, we first performed GIA 13 C calculations using the 3-21G and 6-311G** basis sets on fully optimized (AM1 semiempirical) models of the eight disaccharide for which surfaces were to be derived. The computed 13 C shifts

5 CH 2 H H CH 2 H CH 2 H CH 2 H H H H H CH 2 H H H CH 2 H H D-Glcp-(1 1)-D-Glcp H H H H H CH 2 H H CH 2 H H H D-Glcp-(1 2)-D-Glcp H H H H H CH 2 H H H H D-Glcp-(1 3)-D-Glcp H H H CH 2 H H H H H CH 2 H H H H CH 2 H H H H H H H CH 2 H CH 2 H H H H H CH 2 H CH 2 H H H H H D-Glcp-(1 4)-D-Glcp H H H H CH 2 H CH 2 H NAc NAc CH 3 CNH 2 NHAc CNH 2 NHAc GlcNAc Thr GlcNAc Ser Figure 1. Definition of dihedral angles and, sugar numbering scheme (top), and model compounds (bottom) used in GIA 13 C chemical shift surface calculations.

6 for a total of 48 carbons of the different models were then used in a linear correlation, and the results are summarized in Figure 2. In all cases, the isotropic 13 C chemical shift was obtained by subtracting the isotropic chemical shielding of the 13 C atom to the one found at the same theory level for the methyl carbons of the NMR reference tetramethyl-silane (TMS). Fitting of Raw ab initio Data. Isotropic 13 C shifts for the anomeric carbons obtained as described above were employed in the derivation of equations relating the <,> glycosidic bond dihedral and the 13 C chemical shift. The raw 3-21G ab initio data was scaled and fitted to trigonometric series expansions of general form: i [ j [ A i,j * sinj ( i * ) + B i,j * sin j ( i * ) + C i,j * cos j ( i * ) + D i,j * cos j ( i * ) ] + k [ A i,k * sin( i * ) * cos( k * ) + B i,k * cos( i * ) * sin( k * ) ] ] + C o The data was fitted using Mathematica 3.0 (Wolfram Research, Inc.), using from 91 (i = k = 3, j = 2) to 325 (i = k = 6, j = 2) terms. The results are detailed below.

7 Results and Discussion Scaling of Basis Sets. As seen in Figure 2, GIA calculations using the 3-21G basis set underestimate 13 C experimental values for carbohydrates, a known limitation of GIA methods using small basis sets. 5 However, there is an excellent correlation between results obtained using 6-311G** and 3-21G basis sets (Figure 2). For the C shifts computed, a Pearsons r correlation coefficient of was obtained, indicating that 6-311G** quality results can be obtained by scaling computationally inexpensive 13 C GIA chemical shift calculations using the 3-21G basis set. Furthermore, for the disaccharide trehalose (D-Glcp-α-(1 1)-D-Glcp), whose solution conformation corresponds well with the X-ray and the AM1 optimized structures, 13 there is good correlation between experimental 13 C chemical shift values and those computed at the 6-311G** level of theory (Table 1), indicating the this basis set is adequate for accurate estimations of 13 C chemical shifts in carbohydrates. Therefore, our scaling protocol allows us to obtain good quality chemical shift estimations in a reasonable time, making the determination of the large number of 13 C chemical shift calculations required for the chemical shift surfaces of all the models possible.

8 Cδ6-311G** (ppm) C 6-311G** = * 13 C 3-21G (r= ) Cδ 3-21G (ppm) Figure 2. Correlation of GIA 13 C calculations with 6-311G** and 3-21G basis sets.

9 CH 2 H H H H H CH 2 H H H Carbon atom Experimental 13 C shift Computed 13 C shift Table 1. Comparison of experimental and computed (GIA/6-311G** - AM1 optimized geometry) 13 C chemical shifts (in ppm) for the anomeric carbon (marked orange) of the disaccharide trehalose, D-Glcp-α-(1 1)-D-Glcp.

10 Disaccharide Models. According to several experimental and theoretical studies, there is a periodic dependence between the 13 C chemical shift of the anomeric carbon at the glycosidic linkage and the and dihedral angles. 14 Therefore, we determined chemical shift surfaces for these carbons in the eight model compounds presented in Figure 1. As shown in Figures 3a-d, our results corroborate previous reports. In all cases, continuous surfaces with no singularities were obtained. Furthermore, the 13 C chemical shift surfaces are consistent with the adiabatic energy surfaces of the models. For trehalose, for example, the lowest energy <,> region corresponds well with a region of the chemical shift surface that is in agreement with the experimental range of anomeric 13 C carbon chemical shifts observed for this disaccharide (Figure 4). Glycopeptide Models. ur next set of simulations involved the glycopeptides models GlcNAc Thr and GlcNAc Ser. Using an analogous protocol to the one described above, we obtained the 13 C chemical shift versus <,> surfaces for both models, and two of these are shown in Figure 5. For these models we also analyzed the effect of the peptide conformation on the anomeric carbon chemical shift. Three different surfaces for each model glycopeptide were computed. In one, the conformation of the peptide was allowed to minimize freely during the generation of

11 (a) CH 2 H H H H H CH 2 H H H CH 2 H H H H H H CH 2 H H

12 (b) CH 2 H H H H H CH 2 H H H CH 2 H H H H CH 2 H H H H

13 (c) H H CH 2 H H CH 2 H H H H CH 2 H CH 2 H H H H H H H

14 (d) CH 2 H H H H H CH 2 H H H H H CH 2 H H H CH 2 H H H

15 Figure 3. Anomeric carbon 13 C chemical shift surfaces for model compounds D-Glcp-(1 1)-D-Glcp (a), D-Glcp-(1 2)-D-Glcp (b), D-Glcp-(1 3)-D-Glcp (c), and D-Glcp-(1 4)-D-Glcp (d) in α and β configuration. See text for details.

16 CH 2 H H H H H CH 2 H H H Figure 4. Anomeric carbon 13 C chemical shift (above left) and ab initio potential energy (right) surfaces for trehalose (above right). See text for details.

17 the conformer grid. In the second, the peptide was held in the C 5 (extended) conformation, and in the remaining case, in the α r (α-helical) conformation. The three surfaces obtained for each glycopeptide model were virtually identical, corroborating that the chemical shift of the anomeric carbon is mainly dictated by its local environment. However, if surfaces for the two models are compared, there is a marked difference in the surfaces in the < [ ], [ ]> region. Inspection of the conformers in this region of the 13 C shift surfaces show that van der Waals interactions present in the GlcNAc Thr model, as well as in the disaccharide models, are missing in the GlcNAc Ser model due to the lack of a substituent at the β carbon of Ser. The variation in the chemical shift in this range of dihedral angles between the two glycopeptide models can be explained by differences in the polarization of Sp 3 bonds to the anomeric carbon, which will be reduced in the absence of close van der Waals contacts between the sugar and peptide fragments. Fitting of Raw ab initio Data to Periodic Equations. The periodicity of the surface indicates that functions that reproduces the topology of the chemical shift surfaces could in principle be estimated. Following the methodology of ldfield and coworkers, 6-8 we fitted the raw ab initio 13 C chemical shift data to trigonometric series expansions (see Methods). We found that there is no major improvement in

18 the fit when the number of terms is varied from 91 to 325 (Pearsons r changes from 0.94 to 0.96 in a typical case), indicating that 91 terms suffice to reproduce the ab initio shift surface appropriately. Since this functions relate directly the geometry of the glycosidic bond with the 13 C chemical shift of the anomeric carbon, they could be converted into pseudo-energy penalty terms for direct use during structural refinement. These penalty term functions are usually quadratic: E 13C = K 13C * ( 13 C obs 13 C (, ) calc ) 2 K 13C is a force constant, 13 Cδ obs is the experimental chemical shift and 13 Cδ(,) calc is the chemical shift computed through the empirical equation described above. Since energy minimization and molecular dynamics algorithms compute forces from this pseudo-energy term (first derivatives), its inclusion in simulations simply guides the molecular modeling protocols towards structures in agreement with the experimental 13 C chemical shifts through variation of the and dihedral angles. We have previously applied a similar strategy for structure refinement of peptides from 1 H chemical shift data with excellent results. 15

19 CH 2 H CNH 2 H H NHAc NAc CH 2 H CNH 2 H H NAc CH 3 NHAc Figure 5. Anomeric carbon 13 C chemical shift surfaces for glycopeptide models GlcNAc Ser and GlcNAc Thr. See text for details.

20 Conclusions and Future Direction In this poster we presented results from a series of theoretical studies on the dependence of the anomeric carbon 13 C chemical shift with the glycosidic bond dihedral angles for a representative series of disaccharide and glycopeptide models. ur results are in agreement with experimental observations and earlier theoretical calculations. Some of the features of the chemical shift surfaces can be explained by the presence or absence of van der Waals contacts between fragments of the molecules, which would in turn affect the polarization of the Sp 3 bonds to the anomeric carbon and thus its chemical shift. 16 The mathematical functions derived from the 13 C chemical shift surfaces could be in principle used as an aid in conformational studies, particularly for large polysaccharides, glycoproteins, and glycolipids for which the measurement of NEs and J-couplings can prove experimentally unfeasible. However, exhaustive comparisons between the theoretical results presented here and experimental data are required. We plan to use these functions to back-calculate anomeric 13 C chemical shifts from long molecular dynamics simulations of small polysaccharides and glycopeptides for which extensive NMR data in solution is available. The data from

21 these studies will then be compared statistically to experimental observations. Additionally, we will analyze the effects that the level of structure optimization have in the results of ab initio 13 C chemical shift calculations. Different reports indicate a large dependence between the geometry optimization level and chemical shift estimation, and the use of ab initio optimization of input structures instead of semiempirical methods would be desirable. Finally, we plan to study the qualitative and quantitative differences of 13 C chemical shift calculations in carbohydrates as a function of basis set size and ab initio method, in order to identify the minimum basis set and better suited method required for reliable and cost-effective calculations. ur ultimate goal will be the use of similar methodologies in the study of conformation and dynamics of carrageenans, large natural polysaccharides used extensively in the food and pharmaceutical industries. Acknowledgments This work was partially supported by the NSCA under grant CHE990009N, and used the University of Kentucky HP/Convex Exemplar SPP-2200 supercomputer. The authors also wish to thank Ivana Mihalek, CCS - University of Kentucky, for her invaluable assistance during the initial setup of the shielding calculations.

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