NMR and DFT Analysis of Trisaccharide from Heparin Repeating

Article pubs.acs.org/JPCB

NMR and DFT Analysis of Trisaccharide from Heparin Repeating Sequence Miloš Hricovíni,*,† Pierre-Alexandre Driguez,‡ and Olga L. Malkina§,∥ †

Institute of Chemistry, Slovak Academy of Sciences, 845 38 Bratislava, Slovakia Early to Candidate Unit, Sanofi, 1 Avenue Pierre Brossolette, 91385 Chilly-Mazarin Cedex, France § Institute of Inorganic Chemistry, Slovak Academy of Sciences, 845 36 Bratislava, Slovakia ∥ Faculty of Natural Sciences, Comenius University, 842 15 Bratislava, Slovakia ‡

ABSTRACT: NMR and density functional theory (DFT) have afforded detailed information on the molecular geometry and spin−spin coupling constants of a trisaccharide from the heparin repeating-sequence. The fully optimized molecular structures of two trisaccharide conformations (differing from each other in the form of the central iduronic acid residue) were obtained using the B3LYP/6-311+G(d,p) level of theory in the presence of solvent, the latter included as either explicit water molecules or via a continuum solvent model. NMR spin−spin coupling constants were also computed using various basis sets and functionals and then compared with measured experimental values. Optimized structures for both conformers showed differences in geometry at the glycosidic linkages and in the formation of intramolecular hydrogen bonds. Three-bond proton−proton coupling constants (3JH−C−C−H), based on fully optimized geometry computed using the B3LYP/6-311+G(d,p)/UFF level of theory and hydrated with 57 water molecules, showed that the best agreement with experiment was obtained with the 6-311+G(d,p) basis set and a weighted average of 55:45 (1C4:2S0) of the IdoA2S forms. Other basis sets, DGDZVP and TZVP, also gave acceptable data for most coupling constants, with DGDZVP outperforming the TZVP. Detailed analysis of Fermi-contact contributions to 3JH−C−C−H showed that important contributions arise from oxygen at both glycosidic linkages, as well as from oxygen atoms on the neighboring monosaccharide units. Their contribution to the Fermi term cannot be neglected and must be taken into account for a correct description of coupling constants. The analysis also showed that the magnitude of paramagnetic (PSO) and diamagnetic (DSO) spin−orbit contributions is comparable to the magnitude of the Fermi-contact contribution in some coupling constants in the IdoA2S residue. Calculations of the localized molecular orbital contributions to the DSO terms from separate conformational residues showed that the contribution from adjacent residues is not negligible and can be important for the spin− spin coupling constants between protons located close to the geometrical center of the molecule. These contributions should be taken into account when interpreting DSO terms in spin−spin coupling constants especially in large molecules.

1. INTRODUCTION The structure and dynamics of carbohydrates are mostly analyzed by combining spectroscopic methods, such as NMR spectroscopy, with theoretical analysis. This approach can provide detailed information on 3D carbohydrate structures in solution and their intermolecular interactions. Theoretical analysis often relies on density functional theory (DFT) approaches as molecular structures and energies can be determined at moderate computational cost. Additional data can also be inferred from theoretical interpretations of NMR chemical shifts and spin−spin coupling constants. NMR and DFT have been used for analysis of various saccharide molecules1−5 including glycosaminoglycans (GAGs).6,7 These saccharide derivatives belong to the most intensively studied biologically active saccharides due to their important biological properties and medical applications.7−9 GAG molecules are linear polysaccharides constituted by disaccharide units of a uronic acid and a hexosamine. One of © 2014 American Chemical Society

the most known and studied GAG molecules, heparin, is composed of repeated disaccharidic sequences of a uronic acid (L-iduronic and to a smaller extent D-glucuronic) and Dglucosamine, linked through (1 → 4)-glycosidic bonds. Hydroxyls of these residues can be O-sulfonated at the 2position of uronic acids as well as at the 3- and 6-positions of glucosamine, and amino groups can be N-acetylated, N-sulfated, or nonsubstituted.9 The 3D structures of heparin and heparan oligosaccharides have been the subject of a number of experimental10−18 and theoretical19−31 studies. 3D structures of IdoA2S residues have been intensively studied12,18−23 as these residues have unique conformational properties and play key roles in intermolecular interactions of heparin and heparin sulfate with proteins.9,10,16 The structures of several heparin Received: August 8, 2014 Revised: September 25, 2014 Published: September 25, 2014 11931

dx.doi.org/10.1021/jp508045n | J. Phys. Chem. B 2014, 118, 11931−11942

The Journal of Physical Chemistry B

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Figure 1. Structure of heparin trisaccharide A. The two forms, 1 and 2, correspond to different conformations of the IdoA2S residue (central residue). In 1, the IdoA2S residue is in the 1C4 conformation; in 2, the IdoA2S residue is in the 2S0 conformation. GlcN,6S residues are in the 4C1 conformation. Violet dots represent sodium ions. Solvent (water) molecules are not shown.

linkages Φ (H1′−C1′−O1′−C4) and Ψ (C1′−O1′−C4−H4) for the GlcS,6S−IdoA2S linkage was −60°, −40°; the torsion angles Φ, Ψ for the IdoA2S−GlcS,6S linkage were 80°, 20°. In the skew form 2, the starting Φ, Ψ values for the GlcS,6S− IdoA2S linkage were −40°, −50° and 60°, 20° for the IdoA2S− GlcS,6S linkage. Positions of counterions were based on the previously published X-ray data for structurally similar compounds;35 positions of Na+ ions closed to the 2-SO3− group at the IdoA2S residues were based on starting structures of heparin disaccharide.31 Hydration of trisaccharide molecules was then performed by inclusion of explicit water molecules. The initial positions of the 57 water molecules were based on coordinates of oxygen atoms in water molecules in the published crystal data of sulfated monosaccharides35,36 and the optimized positions of water molecules in heparin disaccharide.31 Full geometry optimization without any constraints was then performed using the B3LYP37 functional and the 6-311+G(d,p)38 basis set (for the solute) and the universal force field (UFF)39 (for the solvent) using GAUSSIAN09.40 The effect of the solvent has also been estimated by polarized continuum model using the CPCM41 approach for comparison. 3JH−H and nJC−H were then DFTcomputed (B3LYP or M06-2X42 functionals) using the 6311+G(d,p), TZVP,43 and DGDZVP44 basis sets. 3JH−H were also computed from the previously described dependence upon torsion angles.45 Averaged coupling constants were obtained by fitting either the DFT-computed coupling constants to experimental values considering the contributions of both conformers 1 and 2 or the coupling constants obtained from the 3JH−H dependence upon torsion angles.45 The calculations of diamagnetic spin−orbit contributions were also done using the deMon program46 with the VWN exchange-correlation functional47 and the IGLO-II basis set.48 The localized molecular orbitals (LMOs) were obtained using the Boys localization.49 Visualization of coupling pathways was performed with the Molekel program50 and the previously published approach.51

oligosaccharides have been mostly analyzed using molecular mechanics (MM)12,14,19 and classical molecular dynamics (MD).20,23,27,29,30 DFT calculations have been performed only on a very few GAG model molecules.22,28,31 The effect of solvent and counterions upon molecular structures is still not well understood. In addition, DFT analysis of NMR parameters, such as proton−proton and proton−carbon spin−spin coupling constants, provides important support in interpretation of experimental data. The present paper deals with NMR and DFT analysis of the trisaccharide A, with the GlcN,6S−IdoA2S−GlcN,6S sequence,32 representing a basic structural motif of heparin. In addition to the analysis of the fully optimized trisaccharide A molecular structure using B3LYP/6-311+G(d,p) in the presence of solvent (the latter included as explicit water molecules or via continuum solvent model), NMR spin−spin coupling constants were computed using various basis sets and functionals and then compared with measured experimental values. Analysis of contributions to spin−spin coupling constants has also been performed. The presented data enable comparison of molecular structures obtained by various solvent models and DFT-computed coupling constants using two functionals and three basis sets. Analysis of Fermi-contact contributions and spin−orbit contributions provides an explanation of measured values of proton−proton and proton−carbon spin−spin coupling constants.

2. METHODS NMR spectroscopy. Trisaccharide A was synthesized according to standard procedures.33 High-resolution NMR spectra were recorded in a 5 mm cryoprobe at 25 °C in D2O on Varian 600 VNMRS spectrometer. One-dimensional 600 MHz 1H and 150 MHz 13C NMR spectra, as well as two-dimensional COSY, HSQC and HMBC, were used for determination of 1H and 13C chemical shifts. Three-bond proton−proton coupling constants (3JH−H) have been determined from 1H spectra. The VNMRJ software was used for deconvolution of less-resolved signals. Long range (nJC−H) proton-carbon coupling constants were measured by gradient-selected high-resolution HMBC.34 Geometry Optimization. In the starting geometry, the LIdoA2S residue was considered in two conformations (1C4, 1, and 2S0, 2, Figure 1) whereas the two D-GlcN,6S residues were in the 4C1 conformations regardless of the IdoA2S form in trisaccharide A. In 1, the starting conformation at the glycosidic

3. RESULTS AND DISCUSSION A. Geometry. Heparin trisaccharide A in aqueous solution was analyzed in two forms, in which the central residue IdoA2S was in the 1C4 conformation (conformer 1) and in the 2S0 conformation (conformer 2) (Figure 1). The geometrical arrangements of both 1 and 2 were influenced by the position 11932



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Table 1. Selected Optimized (B3LYP/6311+(d,p), Explicit Solvent) Interatomic Distances (in Å) in Heparin Trisaccharide Aa residue

bond

GlcN,6SNR

C1−C2 C5−O5 C1−O5 C1−O1 C2−N2 S(N)−N2 S(N)−O21 S(N)−O22 S(N)−O23 OH3−NSO23 OH4−O6 C1−C2 C5−O5 C1−O5 C1−O1 S2−O2 S2−O21 S2−O22 S2−O23 C6−O51 C6−O52 OH3−O3GlcN,6SR OH3−O23 C1−C2 C5−O5 C1−O5 C1−O1 C2−N2 S(N)−N2 S(N)−O21 S(N)−O22 S(N)−O23 OH3−O23

IdoA2S

GlcN,6SR

1 (1C4) 1.547 1.436 1.410 1.416 1.476 1.702 1.514 1.486 1.467 1.890 2.092 1.545 1.436 1.398 1.440 1.638 1.496 1.479 1.470 1.238 1.274 1.832 − 1.535 1.444 1.418 1.404 1.460 1.714 1.500 1.522 1.449 1.686

(HB)b (HB)

(HB)

(HB)

Table 2. Selected Optimized (B3LYP/6311+(d,p), Explicit Solvent) Bond Angles (in deg) in Heparin Trisaccharide Aa

2 (2S0) 1.532 1.428 1.418 1.412 1.472 1.703 1.508 1.500 1.460 2.098 2.203 1.543 1.434 1.416 1.406 1.680 1.480 1.490 1.462 1.260 1.257 − 1.989 1.530 1.442 1.408 1.429 1.466 1.715 1.455 1.489 1.518 2.023

residue

bond angle

1 (1C4)

2 (2S0)

GlcN,6SNR

O5−C1−C2 O5−C1−O1 C1−O1−C4IdoA C2−N2−S(N) O5−C1−C2 O5−C1−O1 C2−O2−S2 C1−O1−C4Glc O5−C1−C2 O5−C1−O1 C2−N2−S(N)

113.0 113.1 123.1 126.5 112.9 113.9 121.7 119.3 111.2 112.9 121.2

109.0 112.1 117.6 126.3 114.4 112.3 121.4 119.4 108.8 111.1 124.6

IdoA2S

GlcN,6SR (HB) (HB)

a

The two forms (1 and 2) correspond to different conformations (1C4 and 2S0) of the IdoA2S residue. The GlcN,6S residues are in the 4C1 conformation.

Table 3. Selected Optimized (B3LYP/6311+(d,p), Explicit Solvent) Torsion Angles (in deg) in Heparin Trisaccharide Aa residue

torsion angle

1 (1C4)

2 (2S0)

GlcN,6SNR

O5−C1−C2−C3 C1−C2−C3−C4 C1−O1−C4−H4IdoA H1−C1−C2−C3 H1−C1−O5−C5 H1−C1−O1−C4IdoA H1−C1−C2−H2 H2−C2−C3−H3 H3−C3−C4−H4 H4−C4−C5−H5 O5−C1−C2−C3 C1−O1−C4−H4GlcN,6S H2−C2−C3−C4 H3−C3−C4−C5 H3−C3−C2−C1 H4−C4−C3−C2 H1−C1−C2−H2 H2−C2−C3−H3 H3−C3−C4−H4 H4−C4−C5−H5 H1−C1−O1−C4GlcN,6S O5−C1−C2−C3 H1−C1−C2−C3 H1−C1−O5−C5 H1−C1−O1−CMe H3−C3−O3−C5 H1−C1−C2−H2 H2−C2−C3−H3 H3−C3−C4−H4 H4−C4−C5−H5

49.5 −42.5 −41.5 167.6 179.5 −68.4 47.5 −163.9 163.0 −168.9 −45.1 21.4 164.6 −168.2 163.5 −167.7 75.1 −74.2 72.3 55.6 87.0 54.7 169.9 −174.0 65.5 −57.9 54.2 174.4 −173.9 −178.3

63.6 −55.6 −47.7 179.2 177.7 −40.7 64.6 175.2 164.8 −162.2 3.3 20.4 102.1 −121.9 97.0 −127.6 123.1 −140.7 115.7 47.5 61.3 62.2 177.8 −179.0 53.2 −70.1 64.6 169.0 166.7 −159.3

(HB)

IdoA2S

(HB)

a

The two forms (1 and 2) correspond to different conformations (1C4 and 2S0) of the IdoA2S residue. The GlcN,6S residues are in the 4C1 conformation. bHydrogen bond.

of counterions and by the solvation environment. Selected optimized interatomic distances, bond and torsion angles are listed in Tables 1−3. The bond lengths (Table 1) in the pyranose rings were comparable to each other in 1 and 2 but differed in the pendant groups or at the glycosidic linkages for all three residues. For example, variations in S−O (in both NSO3− and OSO3− groups) and C6−O (carboxylate) separations arose due to the presence of Na+ counterions in different positions with respect to the oxygen atoms. Interatomic distances in the NSO3− group (nonreducing end GlcN,6SNR residue) revealed that the S−O21 bond was considerably longer (1.514 Å in 1 and 1.508 Å in 2) than the other S−O distances within this group and are comparable to those found in a structurally similar disaccharide.31 The bond lengths for the COO− group suggest resonance bond character of the C6−O51 (1.260 Å) and C6−O52 (1.257 Å) linkages in the IdoA2S residue in 2. On the other hand, quite a large difference in bond lengths was computed for C6−O51 (1.238 Å) and C6−O52 (1.274 Å) in 1 due to different arrangements of the Na+ ions in the different IdoA2S ring conformations. The single bond to double bonds conversion in carboxylate groups

GlcN,6SR

a


thus depended upon Na+ ion positions. The bond elongation was observed when Na+ ions are along the C−O bond. Water molecules also played a role in the geometry of the carboxylates, as has been recently observed in QM/MM dynamics of CH3COO−−water hydrogen bonds.52 In this case the differences between single and double bond lengths were 11933



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Figure 2. Intramolecular hydrogen bonds in trisaccharide A. One interresidue hydrogen bond is between the OH group at C−3 in the IdoA2S ring and the OH group at C−3 and the neighboring reducing-end GlcN,6SR residue (computed distance 1.83 Å). Other three hydrogen bonds are intraresidue in 1 (A). Only intraresidue hydrogen bonds are seen in the 2S0 conformer (2) (B). Part of the water molecules is not shown in the picture for clarity.

Figure 3. Hydrogen bonds among trisaccharide A pendant groups and water molecules from the first shell. Computed separations between X−O··· H−O−H are ∼2.7−3.1 Å (A). Comparable distances are also seen for bifurcated type of hydrogen bonds (B).

also be formed between the 3-SO3− group and the adjacent HN in the central residue in heparin−pentasaccharide.53 As the 3SO3− group was not present in the studied trisaccharide A, such a hydrogen bond could not be observed. The theoretical data presented here, however, indicate that other transient or persistent hydrogen bonds could influence heparin trisaccharide A structure and dynamics. The discrete nature of the explicit water model enabled analysis of water positions located at hydration sites in heparin trisaccharide A. One can expect considerable hydrogen bond interactions between oxygen atoms in trisaccharide (especially those oxygens in sulfate and carboxylate groups) and water molecules. Water molecules can form looser or tighter hydrogen bonds to these oxygens and can compete with intramolecular hydrogen bonds. The presence of Na+ ions also affected formation of intermolecular hydrogen bonds as possible hydration sites were occupied by counterions. The tendency of counterion coordination with oxygens from saccharide and also from water molecules led to some water molecules from the first hydration shell being more “resident” (typically with bifurcated hydrogen atom) than the water molecules not involved in coordination or in hydrogen bonding with saccharide. The computed separations between X−O··· H−O−H were relatively large (∼2.8−3.1 Å, Figure 3A). An approximate comparison exclusively based on these distances,54 not evaluating spherical electron densities,55 suggests that these intermolecular hydrogen bonds are weaker than those

even larger, with average distances of 1.230 Å for the CO bond and 1.368 Å for the C−O bond. However, the geometry in 1 and 2 was influenced by water molecules less than in the CH3COO−−water complex. Theoretical data also showed that all four hydroxyl groups in trisaccharide A formed intraresidue or interresidue intramolecular hydrogen bonds (Figure 2). The hydrogen bond between the OH group at C-3 and the neighboring NSO3− group in GlcN,6S residues in 1 showed the shortest distances (1.686 Å), whereas the same type of bond in 2 had a (C-3)O− H···O−S separation of 2.023 Å. Slightly longer distances (2.092−2.203 Å) were obtained for the hydrogen bond between the OH group at C-4 and O-6 in the hydroxymethyl group in GlcN,6SNR. One interresidue hydrogen bond was formed between the OH group at C-3 in the IdoA2S ring and the OH group at C-3 and the neighboring reducing-end GlcN,6SR residue in 1. This type of hydrogen bond was not present in 2. However, instead of this interresidue hydrogen bond, a new intraresidue hydrogen bond was found in the 2S0 conformer (2), namely between the OH group at C-3 and O-23 at the neighboring 2-SO3− group. These two hydrogen bonds are likely competing with each other and the breakdown of the interresidue IdoA2S(C-3)O−H···O−(C-3) GlcN,6SR hydrogen bond in 1 and formation of the intraresidue IdoA2S(C-3)O− H···O−S(C-2) hydrogen bond in 2 can play an important role in the internal dynamics of trisaccharide A in solution. Recent NMR experimental data indicated that a hydrogen bond could 11934



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Figure 4. Interatomic distances (in Å) between oxygen atoms belonging to trisaccharide A or water molecules, and sodium ions. Oxygen atoms (red) involved in coordination with sodium ion (violet) are displayed as spheres. IdoA2S residues are either in the 1C4 chair form (A) or the 2S0 skew form (B).

Table 4. Computed Three-Bond Proton−Proton Coupling Constants (Values in Hz) in Heparin Trisaccharide Aa

1

residue (conformation)

array of atoms

torsion angle (CPCM)

GlcN,6SNR (4C1)

H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5

48.8 −165.1 162.6 −168.4 76.2 −75.3 73.8 53.0 55.1 173.5 −174.1 −179.2 65.2 173.8 166.9 −162.3 140.3 −150.9 115.9 51.8 52.1 −173.4 163.3 −171.1

IdoA2S (1C4)

GlcN,6SR (4C1)

2

GlcN,6SNR (4C1)

IdoA2S (2S0)

GlcN,6SR (4C1)

3

JH−H TZVP (CPCM)

torsion angle (expl. solv.)

4.41 6.88 6.77 8.20 1.86 2.68 2.93 3.16 3.89 8.99 8.57 7.74 2.59 9.53 7.64 7.29 4.45 5.54 0.63 2.99 5.11 9.63 7.17 8.16

47.5 −163.9 163.0 −168.9 75.1 −74.2 72.3 55.6 54.2 174.4 −173.9 −178.3 64.6 175.2 164.8 −162.2 123.1 −140.7 115.7 47.5 64.6 169.0 166.7 −159.3

3

JH−H TZVP (expl. solv.) 4.25 6.44 7.11 8.50 1.76 2.59 3.11 2.73 4.09 9.15 8.82 7.73 2.88 9.66 7.57 7.66 2.53 3.76 0.72 3.48 2.92 10.60 7.86 7.27

3

JH−H DGDZVP (expl. solv.) 4.16 7.69 8.45 10.25 1.59 2.62 3.14 2.89 4.17 11.95 10.62 9.08 2.81 11.44 8.83 9.22 2.47 4.15 0.48 3.66 2.78 12.46 9.11 8.55

3

JH−H 6311+G (expl. solv.) 4.57 8.00 8.66 10.31 1.72 2.74 3.33 2.64 4.47 11.16 10.67 9.35 3.00 11.57 9.17 9.28 2.81 4.54 0.74 3.66 3.10 12.56 9.52 8.74

a

The two forms (1 and 2) correspond to different conformations (1C4 and 2S0) of the IdoA2S residue. The GlcN,6S residues are in the 4C1 conformation. Data obtained using molecular geometry with the CPCM solvent model and TZVP basis set are in columns 3 and 4. Data obtained using explicit solvent and different basis sets (DGDZVP, TZVP, and B3LYP/6-311+G(d,p)) are presented in columns 5−8.

computed for the CH3COO−−water complex.52 Unlike the CH3COO−−water solution, the present data also indicated that bifurcated, both donor and acceptor, hydrogen bonds could be formed between water molecules and oxygens from sulfate groups (Figure 3B). This arrangement of water molecules influences the structure of the first hydration shell in the vicinity of the sulfate and carboxylate groups. Similarly to heparin-disaccharide,31 Na+ ions showed a tendency toward 6-fold coordination with oxygens from sulfates, carboxylates and water molecules in both 1 and 2. One Na+ ion was coordinated with 3 oxygen atoms from the

pendant groups and 3 oxygens from water in 1, as shown in Figure 4A. Distances between sulfate oxygens and sodium ions varied between ∼2.2 and ∼2.5 Å in both conformers. Somewhat larger separations were obtained for water oxygen···sodium distances (∼2.75−3.69 Å) (Figure 4B). In 2, however, two Na+ ions were coordinated with four oxygens from the pendant groups and two from water molecules (Figure 4B). Bond angles (Table 2) do not differ much between 1 and 2, although some variations (about 5.5°) are seen for the glycosidic linkage (C1−O1−C4IdoA) angle. As expected, 11935



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Table 5. Computed Averaged Three-Bond Proton−Proton Coupling Constants (⟨3JH−H⟩, Values in Hz) in Heparin Trisaccharide Aa residue (conformation) GlcN,6SNR (4C1)

IdoA2S (1C4)

GlcN,6SR (4C1)

⟨3JH−H⟩ 55:45 C4/2S0 CPCM

⟨3JH−H⟩ 55:45 1C4/2S0 expl. solv. TZVP

⟨3JH−H⟩ 55:45 1C4/2S0 expl. solv. DGDZVP

⟨3JH−H⟩ 55:45 from tosion anglesb

⟨3JH−H⟩ 55:45 1C4/2S0 expl. solv. 6311+G(d,p)

3.6 8.1 7.2 7.8 3.1 3.9 1.9 3.1 4.4 9.3 7.9 7.9

3.6 7.9 7.3 8.1 2.1 3.1 2.0 3.1 3.6 9.8 8.4 7.5

3.6 9.4 8.6 9.8 2.0 3.3 1.9 3.2 3.5 12.2 9.9 8.8

3.3 9.6 9.2 9.4 1.9 3.2 1.5 3.7 3.7 9.8 9.7 9.4

3.8 9.6 8.9 9.8 2.2 3.6 2.2 3.1 3.8 11.8 10.1 9.1

1

3

JH−C−C‑H expt. 3.4 10.4 9.1 9.8 2.9 6.2 3.0 3.0 3.6 10.4 9.9 9.2

⟨ JH‑H⟩ were computed either as a weighted average using 3JH−H data presented in Table 4 or as a weighted average of the 3JH‑H values obtained using torsion angles (column 5, Table 4) and the dependence 3JH−C−C‑H = 9.6 cos2 φ − 0.6 cos φ + 0.2.45 Experimental values are presented in the last column. bUsing dependence from ref 45.

a 3

geometry optimized with explicit solvent (2.92 Hz), whereas JH2−C2−C3−H3 in the same residue was smaller. On the other hand, 3JH2−C2−C3−H3 in IdoA2S in 2 was higher (5.54 Hz) than those obtained using explicit solvent geometry (3.76 and 4.54 Hz) and were closer to the experimental data. In general, however, data based on geometry optimized with explicit solvent agreed better with experiment (Table 5) than those based on the continuum solvent model. The quality of the basis set for calculations of 3JH−C−C−H can be seen by comparing the data presented in columns 6−8 in Table 4. Most of the TZVP-computed 3JH−C−C−H values were comparable to those obtained with the 6-311+G(d,p) basis set and in a good agreement with experiment; some coupling constants, however, were clearly smaller. For example, calculated 3JH2−H3, 3JH3−H4 and 3JH4−H5 were 1−2 Hz too small in both GlcN,6S residues. Thus, though the overall trends seen in experiment could be obtained using the TZVP basis set, several couplings were noticeably underestimated. The DGDZVP basis sets gave good data for most coupling constants and outperformed the TZVP basis set. In fact, as mentioned in our previous analysis,31 this relatively simple basis set can give satisfactory data, nearly as good as the data obtained by the more rigorous approach with the 6-311+G(d,p) basis set. The best accordance with the measured 3 JH−C−C−H values was given by the 6-311+G(d,p) basis set and was found to be the most suitable for accurate calculations with relatively acceptable demands on computer time and memory. In addition to the B3LYP functional, the M06-2X functional using the 6-311+G(d,p) basis set has been applied as well. The computed data were found to be worse than those obtained with the B3LYP functional. For example, 3JH1−C1−C2−H2 and 3 JH2−C2−C3−H3 in the GlcN,6SNR residue in 1 were 4.01 and 7.36 Hz respectively, i.e. lower values than would correspond to experiment. 3JH−C−C−H data obtained with the M06-2X/6311+G(d,p) approach will therefore not be discussed further. The best agreement of computed averaged 3JH−C−C−H with experimental values is shown in Table 5. Inspection of the computed results indicates that the best agreement between theory and experiment was obtained using the B3LYP/6311+G(d,p) level of theory and the explicit solvent geometry, using a weighted average of 55:45 of the IdoA2S forms (1:2, i.e. 1 C4:2S0). Averaged 3JH−C−C−H magnitudes for both GlcN,6S

variations in the torsion angles (Table 3) were much larger, with all IdoA2S torsions angles showing significant differences between 1 and 2. The GlcN,6S pyranose rings were in the 4C1 chair form but the ring geometries changed slightly during the minimization procedure and the optimized structures differed from each other in 1 and 2. This is seen in the variations of heavy atoms torsion angles, e.g., O5−C1−C2−C3 (a difference of nearly 18° between 1 and 2 in GlcN,6SR). Similar trends were obtained in hydrogen atom torsion angles as well. Large differences, up to 20° (H3−C3−C4−H4, GlcN,6SR), were seen, and resulted in changes in size of 3JH−H magnitude (Table 4) in the “rigid” GlcN,6S residues. It should also be noted that the effect of the central residue pseudorotation is different for GlcN,6SR and GlcN,6SNR residues. Generally similar variations of this residue were also observed in a structurally related disaccharide.31 As expected, ϕ, ψ torsion angles (H1−C1−O1− C4, H4−C4−O1−C1) at the glycosidic linkage differed from each other in 1 and 2 as well. B. NMR Spin−Spin Coupling Constants. Three−bond proton−proton coupling constants (3JH−C−C−H) in heparin trisaccharide A were computed using the B3LYP/6-311+G(d,p)/UFF fully optimized trisaccharide geometry (hydrated with 57 water molecules) and three basis sets, 6-311+G(d,p), TZVP and DGDZVP. The TZVP basis set was also used for calculation of 3JH−C−C−H using a geometry optimized with continuum solvent model for comparison. Computed coupling constants, together with torsion angles between corresponding proton pairs, are listed in Table 4. As expected, pseudorotation of the IdoA2S residue resulted in variations of 3JH−C−C−H magnitudes as seen in 1 and 2. GlcN,6S residues were in 4C1 chair form in both cases and though these residues did not convert to other conformations, the pyranose rings geometries exhibited noticeable variations in 1 and 2 in both GlcN,6SR and GlcN,6SNR residues. Different geometries of the GlcN,6S rings resulted in different 3JH−C−C−H magnitudes but this did not cause any disagreement between theory and experiment. Comparison of computed 3JH−C−C−H magnitudes (columns 4 and 6) obtained for geometries optimized with continuum and explicit solvent models using the TZVP basis sets show that the differences exist mainly in the GlcN,6SR residues. 3JH1−C1−C2−H2 (5.11 Hz) in the GlcN,6SR residue in 2 for the PCM geometry was much higher than the coupling constants from the

3

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Table 6. DFT-Computed (B3LYP/6311+(d,p)) Fermi Contact, Spin−Dipolar, Paramagnetic Spin−Orbit, and Diamagnetic Spin−Orbit Contributions to the Three-Bond Proton−Proton Coupling Constants (Values in Hz) in 1 and 2a conf. residue 1

4

GlcN,6SNR ( C1)

IdoA2S (1C4)

GlcN,6SR (4C1)

2

GlcN,6SNR (4C1)

IdoA2S (2S0)

GlcN,6SR (4C1)

a

array of atoms

torsion angles

Fermi contact

spin−dipolar

paramgn. spin−orbit

diamgn. spin−orbit

total 3JH−C−C‑H

H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5 H1−H2 H2−H3 H3−H4 H4−H5

47.5 −163.9 163.0 −168.9 75.1 −74.2 72.3 55.6 54.2 174.4 −173.9 −178.3 64.6 175.2 164.8 −162.2 123.1 −140.7 115.7 47.5 64.6 169.0 166.7 −159.3

3.97 8.00 8.73 10.30 1.05 2.28 2.87 1.82 3.92 11.22 10.71 9.40 2.55 11.55 9.17 9.23 2.51 4.38 0.56 2.96 2.67 12.60 9.51 8.75

0.13 0.04 0.04 0.04 0.04 0.03 0.07 0.12 0.12 0.04 0.05 0.04 0.09 0.05 0.04 0.03 0.02 0.02 −0.01 0.13 0.10 0.04 0.04 0.03

−1.27 1.09 1.19 1.04 −1.07 −0.81 −1.05 −2.16 −1.25 1.15 0.93 0.99 −0.97 1.09 1.14 1.05 0.21 0.59 0.11 −1.64 −0.86 1.14 0.98 0.96

1.74 −1.13 −1.30 −1.07 1.70 1.23 1.44 2.86 1.68 −1.25 −1.02 −1.08 1.33 −1.12 −1.19 −1.03 0.09 −0.45 0.08 2.22 1.19 −1.22 −1.01 −1.00

4.57 8.00 8.66 10.31 1.72 2.74 3.33 2.64 4.47 11.16 10.67 9.35 3.00 11.57 9.17 9.28 2.81 4.54 0.74 3.66 3.10 12.56 9.52 8.74

Total 3JH‑C‑C‑H magnitudes are listed in the last column. 3

residues are almost within experimental error. A somewhat bigger difference between computed and measured values was found for 3JH2−C2−C3−H3 in the IdoA2S residue (3.6 Hz vs 6.2 Hz). This disagreement is probably caused by geometry distortions of the IdoA2S residue leading to smaller 3 JH2−C2−C3−H3. The geometry of the IdoA2S ring, flanked by two GlcN,6S residues, was more distorted in trisaccharide A than in heparin disaccharide due to the presence of the additional GlcN,6S residue. This led to the pyranose ring flattening and a decrease of the H2−H3 torsion angle from about 180° in disaccharide to about 140° in trisaccharide A. It should be noted, however, that such ring distortion was not observed in heparin pentasaccharide (manuscript in preparation) where the IdoA2S residue is also flanked by two GlcN,6S residues, one bearing an extra sulfate group at C-3. Data in column 5 were calculated from the previously described dependence upon torsion angles45 using the same ratio of 1C4 and 2S0 conformers of the iduronate residue. Although this dependence gives satisfactory data in most cases, some averaged values showed worse agreement with experiment. In fact, the local electronic environment influenced the magnitudes of experimental coupling constants in a way that could not be fully described by a Karplus-type relationship. Worse theoretical data were obtained using CPCM geometry than with explicit solvent geometry and thus the explicit solvent model appears more suitable for geometry optimization for heparin sacharides. Hydration of polar sulfate and carboxylate groups, and behavior of counterions, seems better described by discrete water molecules. All this indicates that the solute and solvent are interacting strongly with each other and therefore the CPCM approach is not adequate here. It should be noted that in a structurally similar trisaccharide,56 substituted with an extra sulfate group linked to C-3 in GlcN,6SNR, the measured

JH−C−C−H magnitudes differed from those in the trisaccharide A presented here. One extra sulfate group caused quite noticeable changes not only in the central IdoA2S residue but also in both the GlcN,6SNR and GlcN,6SR residues. Analysis of coupling constants using molecular mechanics suggested that the ratio 2S0:1C4 of the IdoA2S forms was 78:22, i.e. the skew form had prevalence in aqueous solution in contrast to the trisaccharide lacking the 3-O-sulfate group at the GlcN,6SNR residue. Fermi contact (FC), spin-dipolar (SD), paramagnetic spin− orbit (PSO) and diamagnetic spin−orbit (DSO) contributions to 3JH−C−C−H in 1 and 2 computed at the B3LYP/6311+(d,p) level are listed in Table 6. The data show that some coupling constants are considerably different from each other though they have comparable torsion angles. 3JH1−H2 (4.47 Hz) in the GlcN,6SR residue in 1 is nearly 2 Hz bigger than 3JH4−H5 (2.64 Hz) in the IdoA2S residue even though the torsion angles between the corresponding protons are nearly the same (54.2° vs 55.6°). An insight into these differences can be given by the analysis of individual contributions to coupling constants (Table 6). The Fermi term is 3.92 Hz in 3JH1−H2 (GlcN,6SR), considerably bigger than in the 3JH4−H5 coupling constant (1.82 Hz) in the IdoA2S residue in 1 (the difference in torsion angles for these two pairs of protons is 1.4°), indicating a difference in the electronic structure in the neighborhood of different protons. The presence of atoms possessing lone pairs (oxygens and, in case of GlcN,6S, nitrogen) makes the electronic structure more complicated. The striking difference in the magnitude of the Fermi-contact contributions for these two couplings can be rationalized in the following way. The presence of a large number of oxygen lone pairs in IdoA2S interacting with the electron density in the neighborhood of the coupled protons results in the delocalization of the electron 11937



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Figure 5. Visualization of spin−spin coupling pathways for 3JH4−H5 in IdoA2S (A), 3JH1−H2 in GlcN,6SR (B) in 1, and 3JH1−H2 in ethane molecule (C). The torsion angle between coupled protons in ethane is 55 deg. The plot shows the difference in the distribution of the total electron density for two states: when the magnetic moments of the coupled nuclei are parallel and antiparallel. Red color represents negative values and blue color represents positive values. The cutoff value is 0.0008 Å. Violet dots adjacent to the trisaccharide molecule represent sodium ions.

Fermi-contact contribution which is no longer dominant (Table 6). Though in most cases the spin−orbit contributions almost cancel each other, in some cases the difference in the diamagnetic contributions is remarkable, for example for 3 JH4−H5 in IdoA2S (2.86 Hz) and for 3JH1−H2 in the GlcN,6SR (1.68 Hz) in conformer 1. We decided to investigate this phenomenon in more detail. In a local version of the deMon program46 we implemented the analysis of the DSO term in terms of contributions from individual localized molecular orbitals (LMOs). The DSO contribution to spin−spin couplings is the expectation value of the DSO operator over the ground state density. Expressing the ground state density as a sum of the densities of LMOs we can naturally split the total DSO term into the LMO contributions. We selected three spin−spin couplings, one from each residue in 1: 3JH1−H2 in both GlcN,6SNR and GlcN,6SR residues, and 3JH4−H5 in IdoA2S. The DSO contributions were computed for all these three coupling constants. Then, for each coupling, we collated the LMO contributions from separate conformational residues. As a criterion for defining to which residue a particular LMO is assigned, we used the distance from the LMO gauge origin to the midpoint between the coupled protons. The results of this analysis are presented in Table 7.

density and thus attenuation of the medium of transmission of the Fermi-contact interaction. To illustrate this statement, for both couplings, we drew an imaginary line connecting the coupled protons and constructed a sphere with its center in the middle of the line and the radius being a half of the distance between the protons. Then we integrated the electron density within each sphere and thus obtained the number of electrons inside. Though the sphere for 3JH4−H5 (IdoA2S) has a bigger diameter (2.429 Å) than for 3JH1−H2 (GlcN,6SR) (2.416 Å), it contains fewer electrons (3.07 versus 4.49. This illustrates the delocalization of the electron density in the neighborhood of H−4 and H−5 in IdoA2S in comparison with H−1 and H−2 in GlcN,6SR. To provide further understanding of the Fermi-contact interaction, we visualized the spin−spin coupling pathways for these two couplings by plotting the coupling deformation density in Figure 5. One can easily see the involvement of lone pairs of different oxygens (especially for 3JH4−H5 in IdoA2S, Figure 5A) in the Fermi-contact interaction. One can also see that the interaction patterns for these couplings differ from each other. For 3JH4−H5 (IdoA2S), the contributions are from electrons at atoms along the coupling path and also from the oxygen lone-pairs from the carboxylate group, the O−H group at C−3 and the oxygens at both glycosidic linkages. However, important contributions are also seen from the O−5 ring oxygen in GlcN,6SNR and the O−H group at C−3 in GlcN,6SR. Without all these contributions of oxygen lone-pairs at neighboring units, the coupling constants could not be correctly described. On the other hand, the topology is completely different for 3JH1−H2 in GlcN,6SR (Figure 5B). In this case, the pattern somewhat resembles that of an ethane molecule (see Figure 5C) and contributions to coupling constants have more local character. This could also explain why some 3JH−C−C‑H values determined using the Karplus-type curve45 deviate from the experimental data (Table 5) more than 3JH−C−C−H directly computed using DFT in heparin trisaccharide A. As already mentioned, though most of the data agreed with experiment, observable deviations were caused by the local electronic environment rendering the model less accurate. Interestingly, for some 3JH−C−C−H values in the IdoA2S residue, the magnitude of paramagnetic and diamagnetic spin− orbit contributions is comparable with the magnitude of the

Table 7. Contributions from Different Conformational Residues to the Diamagnetic Spin−Orbit (DSO) Term for Selected 3JH−C−C‑H Coupling Constants (in Hz) in 1 residue

DSO contr. 3JH1−H2 GlcN,6SNR

GlcN,6SNR IdoA2S GlcN,6SR total DSO

1.053 0.655 0.045 1.753

3

DSO contr. JH4−H5 IdoA2S

DSO contr. 3JH1−H2 GlcN,6SR

0.677 1.644 0.558 2.879

0.053 0.459 1.180 1.692

In all three cases, the contribution from the residue to which the particular protons belong is the largest one (1.053 Hz for 3 JH1−H2 in GlcN,6SNR, 1.644 Hz for 3JH4−H5 in IdoA2S and 1.180 Hz for 3JH1−H2 in GlcN,6SR). This should be expected since the DSO operator scales roughly as 1/R4, where R is the distance from the interacting protons. Therefore, the contribution of the immediate vicinity should dominate. Surprisingly, however, the contribution from the adjacent 11938



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Table 8. Computed (B3LYP/6-311+G(d,p) and TZVP Basis Set) Three-Bond Proton−Carbon Coupling Constants (Values in Hz) in Heparin Trisaccharide A (B3LYP/6-311+G(d,p)/UFF Fully Optimized Geometry, Explicit Solvent)a residue

array of atoms

torsion angles in 1

torsion angles in 2

3 JC−H 6-311 1

3 JC−H 6-311 2

3 JH−H TZVP 1

3 JH−H TZVP 2

⟨3JH−C⟩ 55:45 1/2 1 C4/2S0

expt.

GlcN,6SNR

C5−H1 C3−H1 C1−H3 C2−H4 C5−H3 C4−H2 C5−H1 C5−H3 C3−H1 C1−OMe

179.5 167.6 163.5 −167.7 −168.2 164.6 −174.0 −57.9 169.9 65.5

177.7 179.2 97.0 −127.6 −121.9 102.1 −179.0 −70.1 177.8 53.2

7.10 3.70 3.92 3.87 4.06 3.31 8.07 2.37 5.05 4.82

7.21 4.11 0.18 1.83 1.64 0.10 7.75 1.37 4.30 3.88

6.53 3.45 3.71 3.65 3.84 3.09 7.58 2.39 4.73 4.71

6.76 3.80 0.20 1.69 1.56 0.10 7.27 1.37 3.99 3.86

7.15 3.89 2.42 2.95 2.97 1.87 7.93 1.92 4.71 4.40

6.8 4.9 3.3 4.0 2.9 4.1 6.9 4.6 4.5 4.5

IdoA2S

GlcN,6SR

a


Table 9. DFT-Computed (B3LYP/6311+(d,p)) Fermi-Contact, Spin−Dipolar, Paramagnetic Spin−Orbit, and Diamagnetic Spin−Orbit Contributions to the Three-Bond Proton−Carbon Coupling Constants (Values in Hz) in 1 and 2a conf. residue 1

4

GlcN,6S ( C1) IdoA2S (1C4)

GlcN,6S (4C1)

2

GlcN,6S (4C1) IdoA2S (2S0)

GlcN,6S (4C1)

a

array of atoms

Fermi contact

spin−dipolar

paramgn. spin−orbit

diamgn. spin−orbit

total 3JH−X−C−C

C5−H1 C3−H1 C1−H3 C2−H4 C5−H3 C4−H2 C5−H1 C5−H3 C3−H1 C5−H1 C3−H1 C1−H3 C2−H4 C5−H3 C4−H2 C5−H1 C5−H3 C3−H1

7.08 3.65 3.83 3.78 4.02 3.23 8.08 2.33 5.02 7.19 4.06 0.04 1.74 1.55 0.02 7.75 1.32 4.26

0.06 0.02 0.03 0.03 0.01 0.03 0.06 −0.05 0.01 0.06 0.01 0.07 0.01 0.01 −0.01 0.06 −0.04 0.02

0.16 0.09 0.05 0.02 0.03 0.03 0.21 −0.51 0.13 0.16 0.10 0.04 −0.08 −0.12 −0.23 0.21 −0.47 0.13

−0.20 −0.06 0.01 0.04 0.00 0.02 −0.28 0.60 −0.11 −0.20 −0.06 0.03 0.16 0.20 0.32 −0.27 0.56 −0.11

7.10 3.70 3.92 3.87 4.06 3.31 8.07 2.37 5.05 7.21 4.11 0.18 1.83 1.64 0.10 7.75 1.37 4.30

Total 3JH−X−C−C magnitudes are listed in the last column.

factor affecting the magnitude of DSO contributions and should be taken into account for interpretation of DSO in spin−spin coupling constants in bulky molecules, especially those which contain heavy elements. It should also be noted that total DSO contributions slightly differ from those presented in Table 6. These minute differences are due to different computational methods used for DSO calculations (GAUSSIAN in Table 6 vs deMon in Table 7). Computed 3JH−C−C−C and 3JH−C−O−C values are listed in Table 8. Both types of coupling constants strongly depend upon torsion angles, but similarly to 3JH−C−C−H, stereoelectronic effects considerably influence their values as well. For example, 3 JH3−C3−C2−C1 and 3JH2−C2−C3−C4 are 3.92 and 3.31 Hz, respectively, in the IdoA2S residue in compound 1. However, one would expect the opposite trend considering the magnitudes of the torsion angles (163.5° vs 164.6°). Atomic electronegativities and the effect of oxygen lone pairs in the coupling path also played an important role affecting the coupling constant magnitudes. Such an effect is clearly visible in the magnitudes of 3JH1−C1−C2−C3 and 3JH1−C1−O5−C5 in the GlcN,6S residues in both 1 and 2. Computed (B3LYP/6-

residues is not negligible and is comparable in all three cases, being 0.655 Hz (from IdoA2S) for 3JH1−H2 in GlcN,6SNR, 0.677 and 0.558 Hz for 3JH4−H5 in IdoA2S from GlcN,6SNR and GlcN,6SR, respectively, and 0.459 Hz for 3JH1−H2 in GlcN,6SR (from IdoA2S). Because of the central position of IdoA2S, there are two adjacent residues for 3JH4−H5, while for the other two (3JH1−H2 in both GlcN,6S) only one adjacent residue contributes. Consequently, the largest DSO contribution is for 3 JH4−H5, i.e. for the spin−spin coupling located close to the geometrical center of the molecule. Furthermore, comparison of proton positions within the IdoA2S residue indicates that H4 and H5 are closer to the center of the molecule than other proton pairs (H1−H2, H2−H3, H3−H4). Therefore, H4 and H5 in IdoA2S are responsible for the largest DSO contribution from IdoA2S. Other protons, e.g., H1 and H2 in IdoA2S, are situated closer to the periphery of the residue and, consequently, the contribution from IdoA2S to the DSO part in 3JH1−H2 is smaller (1.061 Hz). The contributions of units farther away are about 1 order of magnitude smaller than those of adjacent ones (e.g., 0.045 Hz for 3JH1−H2 in GlcN,6SNR from GlcN,6SR). This geometrical arrangement seems an important 11939



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311+G(d,p) level of theory) 3JH1−C1−O5−C5 magnitudes ranged between 7.10−8.07 Hz (columns 5 and 6, Table 8) and were in accordance with measured values (6.8 and 6.9 Hz). Computed 3 JH1−C1−C2−C3 magnitudes were 3.70 Hz−5.05 Hz and also correctly reproduce experimental trends (4.5 and 4.9 Hz). Thus, from comparison with the evidence in heparin disaccharide, the influence of electronegativity and the lone pairs has clear effects on the 3JH−C values. It should be noted in this respect that Fermi terms were the most essential contributions to the coupling constant magnitudes, whereas contributions of other mechanisms were nearly negligible (columns 3 and 7, Table 9). This is in contrast to 3JH−C−C−H, where spin−orbit mechanisms had significant influence on the size of the coupling constants.

been computed (B3LYP/6-311+G(d,p) level of theory) using the geometry optimized with a CPCM solvent model. In this case, we also found worse agreement of 3JH−C−C−H values with experiment; the data thus indicate that the solute and solvent strongly interact with each other, and therefore, the CPCM approach should be avoided when modeling solution properties of heparin−oligosaccharides. As some coupling constants were considerably different from each other even though they have similar torsion angles, individual contributions (FC, SD, PSO, DSO) to 3JH−C−C−H were also computed. A detailed analysis performed for 3JH1−H2 (GlcN,6SR) and 3JH4−H5 in the IdoA2S residue in 1 showed that these coupling constants had quite different Fermi terms, 3.92 Hz (3JH1−H2, GlcN,6SR) and 1.82 Hz (3JH4−H5, IdoA2S) respectively, indicating a difference in the electronic structure in these residues. The reason was found to be the arrangement of oxygen lone pairs in IdoA2S. These lone pairs interact with the electrons in the vicinity of the coupled protons, resulting in the delocalization of the electron density and thus attenuating the medium which propagates the Fermi-contact interaction. Analysis also showed that important contributions arise from oxygen lone-pairs from the carboxylate group, the O−H group at C−3 and the oxygens at both glycosidic linkages, as well as from the O−5 ring oxygen in GlcN,6SNR and the O−H group at C−3 in GlcN,6SR. Though these oxygen atoms are on the neighboring units, their contribution to the Fermi term cannot be neglected and, in fact, must be taken into account for correct description of coupling constants. Further analysis also showed that the magnitude of paramagnetic and diamagnetic spin−orbit contributions is comparable with the magnitude of the Fermi-contact contribution in some coupling constants in the IdoA2S residue. Calculations of the LMO contributions to the DSO terms from separate conformational residues showed that the contribution from the adjacent residues is not negligible and is comparable for 3JH1−H2 in both the GlcN,6SNR and GlcN,6SR residues, as well as for 3JH4−H5 in IdoA2S. Because of the central position of IdoA2S, the largest DSO contribution was seen for 3JH4−H5, i.e. for the proton−proton spin−spin coupling located closest to the geometrical center of the molecule. As 3JH1−H2 in both GlcN,6S residues have only one adjacent residue contributing to DSO, their values were smaller. The comparison of proton positions within the IdoA2S residue also showed that this geometrical factor is visible even within the same residue. Thus, as H4 and H5 are closer to the center of the molecule than other proton pairs (H1−H2, H2−H3, H3−H4), the largest DSO contribution is for H4 and H5. These observations led us to the conclusion that the geometrical arrangement can influence the magnitude of DSO contributions and should be taken into account for interpretation of DSO in spin−spin coupling constants in large molecules. Finally, theoretical analysis also showed that stereoelectronic effects also considerably influenced the 3JH−C−C−C and 3 JH−C−O−C values. The effect of oxygen lone pairs in the coupling path has a significant influence on the magnitude of the coupling constants and, consequently, 3JH−C−C−C and 3 JH−C−O−C differ significantly from each other due to the presence of oxygen in the coupling path. Analysis of contributions to these coupling constants also showed that Fermi terms were essential contributions to the coupling constants whereas contributions of other terms were nearly negligible.

4. CONCLUSIONS NMR and DFT analysis have provided detailed information on the heparin trisaccharide A molecular geometry in aqueous solution. Full geometry optimization of the heparin trisaccharide A with 57 water molecules using the B3LYP/6-311+G(d,p)/UFF model was used to provide the structure of conformers 1 and 2. Computed geometries indicated several differences in bond lengths in pendant groups or at the glycosidic linkages for all three residues in conformers 1 and 2. The main reasons for these variations were due to different positions of Na+ ions and water molecules. 1 and 2 also differ from each other in formation of intramolecular hydrogen bonds: the interresidue IdoA2S(C-3)O−H···O−(C-3) GlcN,6SR hydrogen bond was found in 1, whereas the intraresidue IdoA2S(C-3)O−H···O−S(C-2) hydrogen bond was found in 2. As each conformer of the IdoA2S residue has a unique hydrogen bond configuration and the formation of the skew form must be accompanied by breaking the first hydrogen bond in 1 and creating the IdoA2S(C-3)O−H···O−S(C-2) hydrogen bond in 2, the internal dynamics of this trisaccharide must depend on the small energy difference between these two hydrogen bonds in aqueous solution. The explicit water model also allowed analysis of solute−solvent interactions. Water molecules from the first shell formed hydrogen bonds with saccharide pendant groups. Computed distances between X− O···H−O−H indicated that weak bifurcated hydrogen bonds, both donor and acceptor, can be formed. A further interaction, affecting the 3D structures and intermolecular interactions of 1 and 2 is that with counterions. Similar to heparin−disaccharide, Na+ ions were 6-fold coordinated with oxygens from sulfates and water molecules and we found no significant variations in water oxygen···sodium distances between 1 and 2. Computed three-bond proton−proton coupling constants (3JH−C−C−H) in heparin trisaccharide A showed that the best agreement with experiment was obtained with the 6-311+G(d,p) basis set and a weighted average of 55:45 of the IdoA2S forms (1:2, i.e. 1C4:2S0). Other basis sets less demanding on computer time and memory, DGDZVP and TZVP, gave also acceptable data for most coupling constants, with DGDZVP outperforming TZVP. On the basis of the presented data, the 6311+G(d,p) basis set seems most suitable for accurate calculations of this type of compounds, with acceptable demands on computer time and memory. In addition to the three basis sets, another functional for calculation of 3JH−C−C−H values has been applied as well. Comparison of theoretical data obtained with the M06-2X functional (6-311+G(d,p) basis set) showed that the computed data were worse than those with the B3LYP functional. Furthermore, 3JH−C−C−H values have also 11940



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AUTHOR INFORMATION

Corresponding Author

*(M.H.) Telephone: +421-2-59410323. Fax: +421-2-59410222. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from the Slovak Grant Agency VEGA Grant Nos. 2/0100/14 and 2/0148/13, the Slovak Research and Development Agency (Project No. APVV-0483-10) and SP Grant 2003SP200280203. Calculations were performed at the Computing Centre of the SAS using the supercomputing infrastructure acquired in Projects ITMS 26230120002 and 26210120002, both supported by the Research & Development Operational Program funded by the ERDF.

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