Conformational Behavior of Basic Monomeric Building Units of

Our work reports in detail the results of systematic large-scale theoretical investigations of the glycosaminoglycan building units 1-OMe ΔIdoA-2SNa2...
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J. Phys. Chem. B 2007, 111, 2313-2321

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Conformational Behavior of Basic Monomeric Building Units of Glycosaminoglycans: Isolated Systems and Solvent Effect Milan Remko,*,† Marcel Swart,‡ and F. Matthias Bickelhaupt§ Department of Pharmaceutical Chemistry, Comenius UniVersity, OdbojaroV 10, SK-832 32 BratislaVa, SloVakia, Institut de Quı´mica Computational, UniVersitat de Girona, E-1701 Girona, Spain, and Vrije UniVersiteit Amsterdam, Department of Chemistry and Pharmaceutical Sciences, Section Theoretical Chemistry, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands ReceiVed: July 21, 2006; In Final Form: January 8, 2007

Our work reports in detail the results of systematic large-scale theoretical investigations of the glycosaminoglycan building units 1-OMe ∆IdoA-2SNa2 (1; 2H1 and 1H2 forms), 1-OMe GlcN-S6SNa2 (2), 1,4-DiOMe GlcNa (3), 1,4-DiOMe GlcN-S3S6SNa3 (4), 1,4-DiOMe IdoA-2SNa2 (5; 4C1, 1C4, and 2So conformations), and 1,4-DiOMe GlcN-S6SNa2 (6) at the BP86/TZ2P level of the density functional theory. The optimized geometries indicate that the most stable structure of these monomeric units in the neutral state is stabilized via “multifurcated” sodium bonds. The equilibrium structure of the biologically active anionic forms of the glycosaminoglycans studied changed considerably in a water solution. The computed interaction energies, ∆E, of sodium coordinated systems 1-6 are negative and span a rather broad energy interval (from -130 to -590 kcal mol-1). Computations that include the effect of solvation indicated that in water the relative stability of Na+‚‚‚ligand ionic bonds is considerably diminished. The computed interaction energy in water is small (from -20 to -53 kcal mol-1) and negative, that is, stabilizing.

1. Introduction Complex saccharides, which are part of the extracellular environment, play important roles in numerous physiological and pathological processes, such as hemostasis, growth factor control, anticoagulation, and cell adhesion.1-4 Glycosaminoglycans (GAGs) are present in nature as part of various important polymers, such as heparin and heparan sulfate. Heparin and heparan sulfate are heterogeneous polymers consisting of repeating disaccharide sequences of hexuronic acid (D-glucuronic, L-iduronic) and D-glucosamine.5,6 These residues are substituted with N- or O-sulfate groups with various degrees of substitution. Heparan sulfate also has N-acetylated groups in glucosamine residues, and, in general, it is a more heterogeneous polymer than heparin. The chemical heterogeneity of heparin/ heparan GAGs in terms of their sulfation pattern and backbone chemical structure facilitates binding to a variety of proteins such as growth factors, enzymes, and morphogenes.7 Heparin is strongly acidic because of its content of covalently linked sulfate and carboxylic acid groups. In heparin sodium, the acidic protons of the sulfate units are replaced by sodium ions. Heparin sodium is derived from bovine lung tissue. This complex organic acid, which is found especially in lung and liver tissue, has a mucopolysaccharide as its active constituent, prevents platelet agglutination and blood clotting, and is used in the form of its sodium salt in the treatment of thrombosis and in heart surgery. Its antithrombotic activity is explained by the interaction with protein antithrombin III (AT-III).6,8-10 The action of anticoagulants starts when they bind to antithrombin through a group of five subunits (DEFGH). It was found that this unique * To whom correspondence should be addressed. Tel.: +421-250117225. Fax: +421-2-50117100. E-mail: [email protected]. † Comenius University. ‡ Universitat de Girona. § Vrije Universiteit Amsterdam.

pentasaccharide fragment (PS) constitutes the minimal binding domain for AT-III. It contains five O-sulfate groups, three N-sulfate groups, and two carboxylate moieties, which are in the isolated molecule coordinated by 10 sodium cations. In the antithrombin-pentasaccharide complex, these acidic groups are completely ionized and interact with the complementary (Arg, Lys, Glu, and Asn) side chains on the protein.10-14 The preparation of PS and its many analogues led to the establishment of the structure-activity relationships of heparin-like pentasaccharides.10,13 Despite its importance, the three-dimensional (3D) molecular structure of heparin is not known. Likewise, the glycosaminoglycans remain one of the structurally less-well characterized classes of saccharides, despite their interesting properties. The absence of experimental structural data of basic building units of glycosaminoglycans presents a challenge to the application of molecular modeling methods to obtain insight into the recognition and binding processes. Several authors used molecular mechanics and dynamics calculations for investigation of the structure and properties of heparin and heparin-protein interactions.14-17 However, there is still no molecular mechanics force field parametrization capable of adequately reproducing all polysaccharide conformational features.17 The molecular structure of R-L-iduronic acid monomeric structural unit (1,4-DiOMe IdoA-2SNa2) and four dimeric structural units of heparin (D-E, E-F, F-G, and G-H) has been previously investigated18,19 using the density functional theory. However, the solvent effect on the geometrical stability of sodium salts of these structures has not been theoretically examined before. In this paper, we have used large-scale quantum chemical calculations for the study of stable geometries of six monosaccharide units: 1-OMe ∆IdoA-2SNa2 (1), 1-OMe GlcN-S6SNa2 (2), 1,4-DiOMe GlcNa (3), 1,4-DiOMe GlcN-S3S6SNa3 (4), 1,4-DiOMe IdoA-2SNa2 (5), and 1,4-DiOMe GlcN-S6SNa2 (6)

10.1021/jp0646271 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/13/2007

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Remko et al.

Figure 1. Structure and atom numbering of the glycosaminoglycan species investigated.

in both sodium salt and anionic forms (Figure 1: GlcN is glucosamine, IdoA is iduronic acid, GlcA is glucuronic acid, S is sulfate, and Me is methyl). These monosaccharides are basic representative monomeric units of heparin. Of particular interest are the molecular geometries and sodium affinities of the species and how these properties are influenced by solvation. The results of this study are discussed and compared with the available experimental results for structurally related systems and discussed with the present theories of action of these glycosaminogycans. 2. Method of Calculation The input geometries (Figures 1 and 2) of all molecules investigated were constructed using the molecular modeling tool and the definition of approximate values of the conformational parameters for the pyranose ring .20 Geometries of the 1-OMe ∆IdoA-2SNa2 (1; 2H1 and 1H2 forms), 1-OMe GlcN-S6SNa2 (2; 4C1 conformation), 1,4-DiOMe GlcNa (3; 4C1 conformation), 1,4-DiOMe GlcN-S3S6SNa3 (4; 4C1 conformation), 1,4-DiOMe IdoA-2SNa2 (5; 4C1, 1C4, and 2So conformations), and 1,4-DiOMe GlcN-S6SNa2 (6; 4C1 conformation) were fully optimized at the BP86/TZ2P21,22 level of the density functional theory23-25 (DFT) using the Amsterdam Density Functional (ADF)26,27 and QUantum-regions Interconnected by Local Descriptions (QUILD)28,29 program systems. The interaction energy, ∆E, for the reaction of a sodium cation with Lewis bases [nNa+(g) + Ln-(g) f NanL(g)] is given by the following

equation

∆E ) E[(Na+)n‚‚‚Ln-] - {nE[Na+] + E[Ln-]}

(1)

where E[Na+] and E[Ln-] are the energies of the metal cation and ligand molecules, respectively, and E[(Na+)n‚‚‚Ln-] is the energy of the complex. The molecular orbitals (MOsO were expanded in a large uncontracted set of Slater-type orbitals (STOs) (TZ2P),30 which is of triple-ζ quality, augmented by two sets of polarization functions (3d and 4f on C, N, and O; 2p and 3d on H); the core electrons (e.g., 1s for second row, 1s2s2p for third row, etc.) were treated by the frozen core (FC) approximation.31 An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately in each self-consistent field (SCF) cycle. Energies and gradients were calculated using the local density approximation (LDA; Slater exchange and VWN32 correlation) with nonlocal corrections due to Becke33 (exchange) and Perdew22 (correlation) added self-consistently. This exchange correlation (xc)-functional is one of the three best DFT functionals for the accuracy of geometries,34 with an estimated unsigned error of 0.009 Å in combination with the TZ2P basis set. Solvent effects on the species studied were evaluated using the COSMO polarizable continuum model (CPCM).35-37 The structures of all gas-phase and condensed-phase (CPCM) species were fully optimized without any geometrical constraint.

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Figure 2. Conformational flexibility of residues in heparin: (A) 2H1 and 1H2 forms of the 1-OMe ∆IdoA-2SNa2 species, and (B) 4C1, 1C4, and 2So conformations of 1,4-DiOMe IdoA-2SNa2 species studied.

It has been shown previously38 that the COSMO method reproduces hydration energies with accuracy on the order of a few kcal/mol but mostly (70% of the cases) even better than one kcal/mol. 3. Results and Discussion 3.1. Molecular Structures. The Cartesian coordinates (angstroms) of the fully optimized 1-OMe ∆IdoA-2SNa2 (1), 1-OMe GlcN-S6SNa2 (2), 1,4-DiOMe GlcNa (3), 1,4-DiOMe GlcN-S3S6SNa3 (4), 1,4-DiOMe IdoA-2SNa2 (5), and 1,4DiOMe GlcN-S6SNa2 (6) computed at the BP86/TZ2P level of theory are given in Table A of the Supporting Information. Heparinase depolymerization produces at the non-reducing end a terminal uronate with an unsaturated 4,5 carbon bond.39 Crystallographic data show that this residue exists in two different forms 2H1 and 1H2 (Figure 2) within the same unit cell indicating that these are of nearly equal energies.40 Thus, the actual calculations of the 1-OMe ∆IdoA-2SNa2 were carried out with both conformers. The 1,4-DiOMe IdoA2SNa2 molecules are 2-substituted iduronic acids in the L form and the starting conformations of the pyranose ring for optimization were set to the 4C1, 1C4 chair forms and skew-boat 2So conformation (Figure 2). These conformations were taken as they are the prevalent forms, depending on the substitution pattern of this residue and on its relative position in the chain, in heparin, and its derivatives observed in high-resolution NMR spectra.39,41-43 An analysis of the directions in which metal ions approach a carboxyl group in crystal structures showed that the most likely arrangements of metal cations are syn, anti, and bidentate.44 Bidentate (direct) bonding, in which the metal cation is oriented

symmetrically to two oxygen atoms of the functional groups studied, is preferred in the M+‚‚‚O 2.3-2.6 Å separation range.45 In the complexes under study, pairing the negatively charged carboxyl and sulfate groups with the sodium cations represent interactions of this type. The sulfate group in the species investigated is essentially tetrahedral with O-S-O angles ranging from 100 to 107˚. The nitrogen atom of the -NHSO3Na moiety is in all species pyramidal. The structural parameters for the O-S and N-S bonded sulfate groups are very similar. The pattern of the bond lengths S-O(a) and S-O(b) involved in the bifurcated O‚‚‚Na interaction in sodium salts of the saccharide species studied allows them to be recognized as S-O bond types with considerable double bond character. The S-O distances of these interactions are found in the range 1.49-1.51 Å. A substantially shorter S-O(c) bond in sodium saccharides is not involved in coordination with the sodium cation and may be recognized as an SdO bond type with optimal lengths in the range 1.44-1.47 Å. The S-O(c) bond length is similar to the typical SdO (1.536 Å) in (CH3)2SdO computed by us at the BP86/TZ2P level of DFT. Thus, the coordination of sodium cations to the O(a) and O(b) oxygen atoms of the sulfate group via the OO bifurcated bonds in sodium salts of the saccharides under study results in appreciable shortening of the free S-O(c) bond. The length of the S-O bond in the C-O-S linkage (approximately 1.61.7 Å) is significantly different from those of the terminal S-O bonds. In general, the S-OC(2) and S-OC(3) bonds are by about 0.1 Å shorter in comparison with the analogous S-OC(6) bonds. For both carboxylate and sulfate sodium ion complexes, bidentate (direct) bonding was found in the relatively short O‚‚‚Na separation range (2.2-2.3 Å). The

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Figure 3. Gas-phase minimum energy conformation of the 1-OMe ∆IdoA-2SNa2 (2H1 form).

O(a) ‚‚‚Na‚‚‚O(b) angle of the bifurcated sodium bond lies within the relatively narrow interval of 60-70°. Nevertheless, in some structures of the sodium salts studied, Na+ ions are often found surrounded by a cluster of O atoms belonging to the neighboring polar groups of the saccharide. The most prominent example is the 1-OMe ∆IdoA-2SNa2 molecules. Its 2H conformation is in the gas-phase stabilized via the coordina1 tion of the sodium cation with four neighboring oxygen atoms (Figure 3). For the manifestation of the changes in the molecular structure upon dissociation and/or solvent effect, we used the molecular structure of the 1,4-DiOMe GlcN-S3S6SNa3. The superposition of the selected 3D species of this molecule is presented in Figure 4. The presence of three negatively charged groups in this system increases its interaction with the counter ions (Na+) of the surrounding medium. Thus, the dissociation of the respective sodium salt results in structural rearrangements of anions (Figure 4(I)). The solvent (water) changes the conformation of the pyranose ring only slightly, and the original 4C1 conformation is present in both sodium salts and dissociated saccharide species studied (Figure 4(II)). Larger changes upon solvation of the sodium salt are observed in the equilibrium position of the O-sulfated and N-sulfated groups. The same behavior is also noticed in the case of the solvated trianionic species. Upon solvation, the change in the position of the -NH-SO3- group was especially observed. The dissociation of the solvated 1,4-DiOMe GlcN-S3S6SNa3 results in a trianion with almost the same geometry of the pyranose ring. For the relaxed structure of the trianion is, however, the different position of the side O-sulfated and N-sulfated groups, respectively, characteristic. The solvation is accompanied by the noticeable conformational change of the C(2)NH-SO3- group (Figure 4(III)). The C(2)N-sulfo groups in the biologically active pentasaccharide unit (DEFGH) are one of the essential groups for the activation of AT-III.10 However, the spatial orientation of basic residues, rather than sequence proximity, is an important factor in determining heparin-binding ability to interact with heparinbinding protein.8 Large conformational rearrangement of the O-sulfated and N-sulfated groups of the basic glycosaminoglycans is connected with substantial release of entropy, which in turn may reduce the enthalpic contribution of the heparin chains in the thermodynamic analysis of the heparin-protein complex.46 1-OMe ∆IdoA-2SNa2 (unit A). For di- and oligosaccharides that have been studied by NMR,47,48 proton-coupling constants for this terminal uronate indicate conformational flexibility and the existence of two stable conformers (1H2 and 2H1). The initial conformations (1H2 and 2H1) were taken from the heparinderived tetrasaccharide structure given by Mikhailov et al. ,39

Remko et al. and the X-ray data of the strontium 4-O-(4-deoxy-β-Lthreo-hex-4-enosyl)-D-galacturonate.40 The 4,5-unsaturated pyranose building unit of heparin represents a relatively rigid structure with coplanar C(3), C(4), C(5), and O(5) atoms. The two stable 1H2 and 2H1 conformations are differentiated by above- and below-plane positions for C(1) and C(2) atoms (Figure 2). The optimized conformations in the gas phase are stabilized by means of intramolecular hydrogen bonds. The intramolecular C(3)O-H‚‚‚OC(4) hydrogen bond with lengths of 2.1-2.5 Å stabilizes the optimized structure of the 1H2 conformer in sodium salt and dianion species, and it is present also in the solvated systems. For the 2H1 conformation, the existence of such hydrogen bond is, for reasons of stereochemistry, impossible. However, the gas-phase anion and both the solvated sodium salt molecule and solvated dianion of the 2H1 conformation are stabilized by a strong intramolecular hydrogen bond C(3)O-H‚‚‚O-S with the H‚‚‚O distances found in the range 1.8-1.9 Å. The sodium cations are dicoordinated to the anionic carboxylate and O-sulfate groups (1H2 conformer). On the other hand, for the 2H1 conformation of the sodium salt, the presence of the tridentate complex is characteristic in both phases, as shown for the solvated complex on Figure 5. 1-OMe GlcN-S6SNa2 (unit D). The pyranose ring of this substituted monosaccharide is in the 4C1 form. Examination of the space model by the 1-OMe GlcN-S6SNa2 complex shows that an alignment of the two groups, the O-sulfate and N-sulfate group, leads to interactions with the sodium cations as a bidentate complex (Figure 5). The equilibrium structure of this complex in gas phase is stabilized by means of two intramolecular hydrogen bonds. The five-membered intramolecular C(3)O-H‚‚‚OC(4) hydrogen bond has a length of 2.35 Å, which is less than the sum of the van der Waals radii49 of hydrogen and oxygen atoms (2.7 Å). The second intramolecular hydrogen bond results from the strong interaction of the negatively charged oxygen atom of the C(6) O-sulfate group with the C(4)OH group of the saccharide moiety. The strong electrostatic attraction in this intramolecular C(4)O-H‚‚‚O-S hydrogen bond results in much shorter optimal hydrogen bond distance of 1.83 Å. These intramolecular hydrogen bonds also stabilize the gas-phase and solvated dianionic molecules and solvated salt. The sodium cations form with the sulfate anions symmetrical bifurcated bonds with O‚‚‚Na distances of 2.22 Å (N-sulfate) and 2.25 Å (O-sulfate). Hydration causes slight prolongation of these bonds. For the solvated 1-OMe GlcN-S6SNa2 complex, the O‚‚‚Na distances were found slightly longer (by about 0.15 Å) than the analogous O‚‚‚Na lengths in the gas-phase complex. 1,4-DiOMe GlcNa (unit E). The calculations were carried out with the 4C1 conformation (Figure 5). In the sodium complex, the sodium cation symmetrically bridges the two oxygens of the carboxylate group. The O‚‚‚Na length found in the gas-phase molecule (2.21 Å) is in the solvated system slightly elongated (at the 2.33 Å). The sodium cation coordinates both anionic oxygens in the plane of the O-C-O moiety. In both the sodium salt and the carboxylate anion, the intramolecular hydrogen bond C(3)O-H‚‚‚OC(2) with optimal distances in the range 2.3-2.4 Å are present. These hydrogen bonds are present also in the solvated molecules. 1,4-DiOMe GlcN-S3S6SNa3 (unit F). The 1,4-DiOMe GlcN-S3S6SNa3 represents the most sulfated residue in heparin. The pyranose ring of this unit is in the 4C1 form.9 The structure in the gas phase is stabilized by the system of metal bonds formed between sodium cations and negatively charged R-SO3- groups of saccharide. Both O-sulfate groups form bifurcated bonds with the sodium cation. The conformationally

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Figure 4. Molecular superimposition of the 1C4 conformations of the 1,4-DiOMe GlcN-S3S6SNa3 and its dianion optimized in the gas phase and of the solvated structure that was optimized in solution: gas-phase sodium salt and its anion (I), solvated phase sodium salt and its anion (II), and gas-phase anion and solution conformation of anion (III).

more accessible C(2)NHSO3- group is involved in the tridentate complex in which all three O‚‚‚Na lengths are close to each other (about 2.25-2.39 Å). In the solvated salt, the same, but slightly elongated, system of the O‚‚‚Na bonds is present (Figure 5). The NH group of the N-sulfate of all four structures, but the gas-phase anion, takes part in the weak intramolecular hydrogen bond C(1)O‚‚‚H-NC(2) at a relatively long separation range (2.3-2.4 Å). 1,4-DiOMe IdoA2SNa2 (unit G). Substituted iduronic acid derivatives represent the simplest models for the L-iduronic acid residues in biologically important heparin, dermatan sulfate, and heparan sulfate.4,8 The conformational structure of this residue in both neutral and ionized states was investigated using 1,4-DiOMe IdoA2SNa2 systems. The 1,4-DiOMe IdoA2SNa2 molecule models unit G of a typical fragment of heparin, in which two neighboring (units F and H) structural units of heparin bound by the (1-4) glycosidic bonds are substituted by the methyl groups. Some trends are apparent. Examination of the space models by the 4C1, 1C4, and 2So conformations of the 1,4-DiOMe IndoA2SNa2 indicates that these conformations are also preserved in the resulting fully optimized structures. The relevant structural parameters of three conformations of the 1,4-DiOMe IndoA2SNa2 are presented in Table A of the Supporting Information. The sodium cation of the -OSO3-‚‚‚Na+ group is always tridentated in gas-phase optimized complexes. In the 4C1 and 1C4 chair conformers and skew-boat 2So conformation, this Na+ atom is in coordination with the O-C(1) oxygen atom. However, our previous calculations using the B3LYP/6-311++G(d,p) model chemistry shows that the skew-boat 2So conformation of the 1,4-DiOMe IndoA2SNa2 molecule may also be stabilized via the coordination of the sodium cation to the oxygen atom of the C(3)OH group.18 This hydroxyl group is involved in intramolecular hydrogen bonds in the gas-phase species. In the 4C1 conformation, an intramolecular hydrogen bond C(3)O-H‚‚‚O-C(4)SO3Na with optimal length of 2.18 Å is present. The 2So conformation in the gas phase is stabilized via intramolecular hydrogen bond C(3)O-H‚‚‚O-C(2)SO3Na with optimal lengths of 2.2 Å. In the gas-phase 1C4 conformation at the BP86/ TZ2P21,22 level of the DFT, no intramolecular hydrogen bonds were found. The carboxyl group in the 4C1, 1C4, and 2So conformations is always dicoordinated and almost symmetrically bonded to both oxygen atoms of the carboxyl group. The system of coordination of the sodium cations by the electronegative oxygen atoms is also preserved in the 4C1 and 2So solvated species (Figure 5). The hydration of the 1C4 chair conformer is connected with the large conformational change of the

C(2)OSO3Na group resulting in the breakage of the Na‚‚‚OC(1) coordination bond. In general, hydration of the 4C , 1C , and 2S conformers caused appreciable geometry 1 4 o changes, especially for substitutents and hexopyranose ring of the skew-boat 2So conformer. In most cases, considerable lengthening of the sodium O-‚‚‚Na+ bonds (by about 0.1-0.3 Å) upon hydration is observed. 1,4-DiOMe GlcN-S6SNa2 (unit H). The 1,4-DiOMe GlcN-S6SNa2 molecules represent the reducing end unit of the pentasaccharide. The gas-phase optimized structure of the sodium salt contains bifurcated symmetric bonds with the sodium cations situated at the opposite parts of the pyranosyl residue. In both cases, the direct (bifurcated) complexes, where the cation is equidistant and interacts with two oxygen atoms at the optimal O‚‚‚Na distance of 2.23 Å, emerge from geometry optimization as the most stable species. For the solvated sodium ion complex, the optimal O‚‚‚Na distances were found slightly longer (2.37 Å); see Figure 5. This lengthening of the O‚‚‚Na length in the sodium salts of the solvated saccharides could be explained by the fact that the hydration of sodium cations and anionic species results in a diminution of the direct electrostatic and ion-dipole interactions. The free hydroxyl group of both salt and its dianion is involved in the intramolecular C(3)O-H‚‚‚NC(2) hydrogen bond with the length of about 2.23 Å. This hydrogen bond occurs also in the solvated species. The optimal geometrical parameters of molecules computed within the COSMO polarizable continuum model (CPCM) and solvent water do not considerably differ from those obtained for isolated molecules (Figure 3). In the absence of experimental gas-phase and aqueous solution data, the geometry of the parent saccharides can be compared only with X-ray data on simpler sulfated monosaccharides.50-52 Lamda et al. determined the crystal and molecular structure of sodium salts of several sulfated galactopyranoses and glucopyranoses.50,51 The sulfate group is essentially tetrahedral with O-S-O angles ranging from 100.6 to 115.5°. The experimental value of the angle C(2)-N-S in N-sulfates (118.0°) is similar to that found in the O-sulfates for the sequence C-O-S (average 119(2)°). The sodium cation has an octahedral coordination. The sodium-tooxygen distances are on average 2.38 Å. Although both methods are based on different models, the computed geometry of the carboxylate, N-sulfate, and O-sulfate moieties of monosaccharide units of heparin (Table A of the Supporting Information) is in good agreement with the experimentally determined X-ray structures for simpler sulfated saccharides. The three basic conformations (4C1, 1C4, and 2So) of the IdoA2S structural unit of heparin, its anionic forms, and sodium salt were also

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Figure 5. Lowest-energy structures of the solvated-phase saccharides studied. Sodium cations are in purple.

Remko et al.

Conformational Behavior of Glycosaminoglycans TABLE 1: Relative Energies (kcal/mol) and Observed Intramolecular Hydrogen Bonds of the 1-OMe ∆IdoA-2SNa2 and 1,4-DiOMe IdoA-2SNa2 Species Studied species 1

H2 sodium salt anion 2 H1 sodium salt anion 4

C1 sodium salt anion 1 C4 sodium salt anion 2 So sodium salt anion

∆Egas-phase

∆Esolv

hydrogen bond

1-OMe ∆IdoA-2SNa2 6.1 -1.0 C(3)O-H‚‚‚OC(4)a,b 5.1 0.9 C(3)O-H‚‚‚OC(4)a,b 0 0 C(3)O-H‚‚‚-O-SC(2)a 0 0 C(3)O-H‚‚‚-O-SC(2)a,b 1,4-DiOMe IdoA-2SNa2 14.3 5.2 C(3)O-H‚‚‚OC(4)a,b 6.2 7.7 C(3)O-H‚‚‚OC(4)a,b 6.7 2.1 1.4 -1.3 C(3)O-H‚‚‚OC(1)a 0 0 C(3)O-H‚‚‚OC(2)SO3Naa,b 0 0 C(3)O-H‚‚‚OC(2)SO3a,b

a Hydrogen bonds in gas-phase conformations. b Hydrogen bonds in solvated system.

systematically studied using the B3LYP/6-311++G(d, p) and B3LYP/6-31+G(d) model chemistries.18 The most stable structure of these molecules corresponds to the skew-boat 2So conformation. This form is also the most stable in water solution. The 2So conformation of sodium salt molecules is not maintained in the anionic species. With the anions, both the 1C4 and 4C1 conformations are present. The relative stability of individual species of the substituted iduronic acid leads to extra stabilization by means of intramolecular hydrogen bonds.18 The solid-state structure of saccharides can be affected by so-called packing effects, which can distort the structure. Since both methods are based on different models, the general structural motifs of the 1-OMe ∆IdoA-2SNa2, 1-OMe GlcN-S6SNa2, 1,4-DiOMe GlcNa, 1,4-DiOMe GlcN-S3S6SNa3, 1,4-DiOMe IdoA-2SNa2, and 1,4-DiOMe GlcN-S6SNa2 can be compared with results from theoretical methods only. 3.2. Relative Energies. The relative energies of individual conformations of the 1-OMe ∆IdoA-2SNa2 (2H1 and 1H2 forms) and 1,4-DiOMe IdoA-2SNa2 (4C1, 1C4, and 2So conformations) with respect to the most stable species computed for the gasphase and solvated molecules are reported in Table 1. The calculations were performed for the sodium salts, which represent the actual species in drug formulations of heparin and its derivatives, and for physiologically active anions. An NMR solution conformation investigation of the heparin-derived saccharide has shown that the uronate (A) residue is predominantly represented by 1H2 conformation with a minor contribution from the 2H1 form .39,43 Our calculations show that this conformer is the most stable species in water solution (Table 1). The 2H1 form is less stable by 1 kcal mol-1. The calculated populations at 310.2 K for the 1H2 and 2H1 conformations are in the ratio 84:16. However, a different situation exists in the gas phase. The 2H1 conformation is the exclusive species (both sodium salt and dianion). In the case of anions, the aqueous phase also favors the 2H1 conformer (Table 1). The intramolecular hydrogen bond C(3)O-H‚‚‚O-SC(2) is responsible for the greater stability of the 2H1 conformation in the isolated state. Both the sodium salt and dianion of the 1H2 conformation are stabilized by the anomeric intramolecular hydrogen bond C(3)O-H‚‚‚OC(4). This hydrogen-bonded contact is, however, much longer (by about 0.7 Å) than the C(3)O-H‚‚‚O-SC(2) hydrogen bond in the 2H1 conformer and therefore much weaker. Previous experimental NMR and theoretical studies have shown that the iduronic acid pyranose bearing a sulfate group at C(2) is a rather flexible structure with the chair 1C4 and skewboat 2So preferred conformations.7,13,18,53 Our previous B3LYP/

J. Phys. Chem. B, Vol. 111, No. 9, 2007 2319 6-311++G(d,p) calculations for compounds 1,4-DiOMe IdoA2S and 1,4-DiOMe IdoA2SNa2 resulted in the skew-boat 2So most stable structure.18 This conformer was also found to be the most stable one in water solution using the Poisson-Boltzmann solver of Jaguar.18 The skew-boat 2So conformation of the 1,4-DiOMe IdoA2SNa2 was also found to be the most stable species (in both the gas phase and solvated state) from the BP86/TZ2P calculations (Table 1). The relative stability of individual conformations of 1,4-DiOMe IdoA2SNa2 decreases as follows: 2So > 1C4 > 4C1 (gas phase and solvated structure). Hydration gives rise to the appreciable reduction of the relative energies of these conformers. The relative stability of the three 1,4-DiOMe IdoA2SNa2 conformations investigated is prevailingly influenced by the occurrence of intramolecular hydrogen bonds formed by the C(3)OH group and the selective coordination of the Na+ cations to individual oxygen coordination centers of the conformers studied (as it is also discussed in the preceding section). The fact that heparin’s biologically active form is polyanionic suggests that the interaction between heparin and proteins is predominantly electrostatic.8 Thus, the situation with anionic species is more interesting than the nonphysiological state of neutral salt. The most stable 2So conformation of sodium salt molecules is not maintained in the solvated anionic species. The 1C conformation was computed to be the most stable one in 4 solvated anions (Table 1). The results of our calculations are in good agreement with experimental findings about the stereochemistry of the pyranose ring of the iduronic acid. Unsubstituted iduronic acid exists predominantly in the 1C4 form,53,54 and the iduronic acid building unit of heparin bearing a sulfate group at C(2) prefers the 1C4 and 2So conformations.55,56 3.3. Gas-phase and Solvated State Sodium Affinities. The calculated gas-phase and solvated state Na+ affinities (interaction energies) of the 1-OMe ∆IdoA-2SNa2 (2H1 and 1H2 forms), 1-OMe GlcN-S6SNa2, 1,4-DiOMe GlcNa, 1,4-DiOMe GlcN-S3S6SNa3, 1,4-DiOMe IdoA-2SNa2 (4C1, 1C4, and 2So conformations), and 1,4-DiOMe GlcN-S6SNa2 are given in Table 2, both for the overall reaction nNa+ + Ln- f NanL and per Na+ cation. These derivatives contain carboxyl and sulfate groups in the neutral state coordinated by the sodium cations and thus may undergo dissociation reactions. It is well-known8 that the polyanion of heparin is bound to the protein active site and therefore represents the active species. The gas-phase dissociation energies, ∆Egas, of the individual monomers are different and very high (Table 2). These sodium affinities represent values for the dissociation of several sodium monocations from their binding sites (carboxyl and sulfate groups). For the purpose of comparison of the contribution of the individual Na+ cations to the interaction energies, the sodium affinity per Na+ cation is also presented. The largest interaction energy per Na+ cation was found for the 1,4-DiOMe GlcNS3S6SNa3. The gas-phase conformation of this molecule is stabilized by the system of the extended coordination bonds occurring between three sodium cations and the oxygen atoms of the substituents. In addition to electrostatic interactions, the dielectric properties of the environment play an important role in the process of the metal cation binding. The interaction energies for sodium cation binding to the anionic species studied in aqueous solution are also listed in Table 2. In the gas phase, the binding reactions could happen with high binding energies (Table 2). This is due to the strong attractive Coulombic interactions between the oppositely charged Na+ cations and the anionic carboxylate and sulfate groups, respectively. The interaction energy in the gas

2320 J. Phys. Chem. B, Vol. 111, No. 9, 2007

Remko et al.

TABLE 2: Calculated Gas-phase and Solvated-phase Interaction Energies (in kcal/ mol) of the Sodium Coordinated Systems for the Overall Reaction nNa+ + Ln- f NanL and Per Na+ Cation ∆Egas no. 2

1a H1 1b 1H2 2 3 4 5a 2SO 5b 4C1 5c 1C4 6 a

system 1-OMe ∆IdoA-2SNa2 1-OMe GlcN-S6SNa2 1,4-DiOMe GlcNa 1,4-DiOMe GlcN-S3S6SNa3 1,4-DiOMe IdoA-2SNa2 1,4-DiOMe GlcN-S6SNa2

∆Ewater,a

overall

per Na+

overall

per Na+

-309.6 -308.6 -236.0 -134.8 -589.2 -312.2 -320.2 -306.8 -282.2

-154.8 -154.3 -118.0 -134.8 -196.4 -156.1 -160.1 -153.4 -141.1

-33.8 -35.8 -29.0 -19.4 -53.4 -37.4 -34.8 -34.0 -30.0

-16.9 -17.9 -14.5 -19.4 -17.8 -18.7 -17.4 -17.0 -15.0

Interaction energy in water computed with the COSMO polarizable continuum model (CPCM).

phase is about 10 times larger in magnitude than that in a polar solvent (water). The interaction energies in water solution are low and negative, that is, stabilizing. This is because the dissociated situation with separate cations and anions gains significantly more electrostatic stabilization by the solvent than the combined, overall sodium salt complex. The dissociation of the sodium salts of the monomers A, D, E, F, G, and H is associated with considerable conformational rearrangements in the ionic species. These rearrangements cause additional energetic stabilizations of the anionic species. Heparin has been recognized to bind to the receptor proteins mostly through its anionic (carboxylate, N- and O-sulfate) groups of the unique pentasaccharide moiety.8 Thermodynamic analyses of the dissociation reactions in the monomeric unit of heparin18 (1,4-DiOMe IdoA2SNa2) have shown that the breaking of the sodium bonds in the glycosaminoglycans is costly in terms of enthalpy but results in an appreciable gain in entropy. It is assumed that much of the Gibbs energy of interaction of heparin and its derivatives with proteins derives from the entropically favorable release of Na+ ions (similar to the situation for DNA).8 However, the sodium ion affinity of glycosaminoglycans is greatly affected by the site’s structural features, stereochemical effects, and the type of intramolecular noncovalent interactions that can be supported at or near the binding group. More detailed calculations of the interaction enthalpies and Gibbs energies of the sodium salts of the A, D, E, F, G, and H are also in progress in our laboratory.

anionic species. With anions, the 1C4 conformation is the most stable species. (3) The gas-phase sodium-cation dissociation energies, ∆Egas, of the individual monomers span a rather broad energy interval (from -130 to -590 kcal mol-1). The largest interaction energy per Na+ cation was found for the 1,4-DiOMe GlcN-S3S6SNa3. The sodium-cation interaction energies in water solution are low but still negative, that is, stabilizing. This is because the dissociated situation with separate cations and anions gains significantly more electrostatic stabilization by the solvent than the combined, overall neutral complex. Acknowledgment. This work has been supported by the European Union HPC-Europa Transnational Access Programme at SARA Amsterdam (M.R.), by the Science and Technology Assistance Agency under Contract No. APVT-51-034504 (M.R.). The work has been also supported by Slovak Grant Agency VEGA Contract No. 1/4301/07 (M.R.). The authors acknowledge the Stichting Academisch Rekencentrum Amsterdam (SARA) for the use of its resources and for excellent support. M.R. thanks the Department of Chemistry, Free University of Amsterdam, for its hospitality during his study stay in Amsterdam. Supporting Information Available: Table showing the Cartesian coordinates of all the gas-phase sodium salt species investigated. This material is available free of charge via the Internet at http://pubs.acs.org.

4. Conclusions This theoretical study set out to determine stable conformations of 1-OMe ∆IdoA-2SNa2 (2H1 and 1H2 forms), 1-OMe GlcN-S6SNa2, 1,4-DiOMe GlcNa, 1,4-DiOMe GlcN-S3S6SNa3, 1,4-DiOMe IdoA-2SNa2 (4C1, 1C4, and 2So conformations) 1,4-DiOMe GlcN-S6SNa2 monomers, and their ionized forms. For these species, experimental physicochemical data that consider their chemical and biological importance are scarce. The following conclusions can be drawn. (1) In the gas-phase, the 2H1 conformation of the uronate (A) residue is by 6.1 kcal mol-1 more stable than the 1H2 form. Examination of the solvent effect (using the COSMO model) has shown that in water the relative stability order of individual conformers (2H1 and 1H2 forms) is not preserved. This residue in water is predominantly represented by the 1H2 conformation with a minor contribution from the 2H1 form. The 2H1 form is less stable in water solution by about 1 kcal mol-1, and thus, both conformations may coexist. (2) The most stable structure of the sodium salt of the heparin unit G corresponds to the skew-boat 2So conformation. This form is also most stable in water solution. The most stable 2So conformation of sodium salt molecules is not maintained in the

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