Glycosaminoglycan conformation: do aqueous molecular dynamics simulations agree with x-ray fiber diffraction?

Andrew Almond1 and John K. Sheehan

School of Biological Sciences, University of Manchester, 2.205 Stopford Building, Oxford Road, Manchester M13 9PT, UK

Received on August 9, 1999; revised on October 5, 1999; accepted on October 5, 1999.


    Abstract
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Glycosaminoglycan–protein interactions are biologically important and require an appreciation of glycan molecular shape in solution, which is presently unavailable. In previous studies we found strong similarity between aqueous molecular dynamics (MD) simulations and published x-ray diffraction refinements of hyaluronan. We have applied a similar approach here to chondroitin and dermatan, attempting to clarify some of the issues raised by the x-ray diffraction literature relating to chondroitin and dermatan sulfate. We predict that chondroitin has the same ß(1->4) linkage conformation as hyaluronan, and that their average ß(1->3) conformations differ. This is explained by changes in hydrogen-bonding across this linkage, resulting from its axial hydroxyl, causing a different sampling of left-handed helices in chondroitin (2.5- to 3.5-fold) as compared with hyaluronan (3.0- to 4.0-fold). Few right-handed helices, which lack intramolecular hydrogen-bonds, were sampled during our MD simulations. Thus, we propose that the 8-fold helix observed in chondroitin-6-sulfate, represented in the literature as an 83 helix (right-handed), though it has never been refined, is more likely to be 85 (left-handed) helix. Molecular dynamics simulations implied that 4C1 and 2SO, but not 1C4, forms of iduronate could be used in refinements of dermatan x-ray fiber diffraction patterns. Current models of 8-fold dermatan sulfate chains containing 4C1 iduronate refine to right-handed helices, which possess no intramolecular hydrogen-bonds. However, MD simulations predict that models containing 2SO iduronate could provide better (85 helix) starting structures for refinement. Thus, the 8-fold dermatan sulfate refinement (83 helix) could be in error.

Key words: glycosaminoglycan/x-ray diffraction/dermatan sulfate/molecular dynamics/water


    Introduction
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Chondroitin sulfate, dermatan sulfate, and hyaluronan are members of the glycosaminoglycan family of extracellular matrix polysaccharides. Their unsulfated forms consist of disaccharide repeats of hexosamine and uronic acid residues. Hyaluronan is a repeating disaccharide of N-acetyl-glucosamine and glucuronic acid. Chondroitin, which contains N-acetyl-galactosamine, differs from hyaluronan by epimerization of a single hydroxyl group, and chondroitin is converted to dermatan by the action of a carboxyl-epimerase.

Unlike hyaluronan, chondroitin and dermatan are not found free in the extracellular matrix, but are covalently linked to protein in complexes such as proteoglycans. Chondroitin sulfate proteoglycans have been localized to cartilage, bone, cornea, and intervertebral disc, whereas dermatan sulfate proteoglycans are found in skin and aorta. Dermatan and chondroitin sulfate have been implicated in interacting with collagen to stabilize the extracellular matrix, binding to growth factors with a high degree of specificity to regulate growth factor activity, and have also been shown to have anticoagulant, antilipemic, antiangiogenic, and antitumor activities (Hardingham and Bayliss, 1990Go; Hardingham and Fosang, 1992Go).

The interaction of carbohydrates with molecular water is central to their biological functions, but is not well understood presently. Molecular dynamics (MD), performed with explicit inclusion of solvent, is an excellent technique for studying these interactions. MD has previously been used to provide detailed information about the water structure around monosaccharides (Brady, 1989Go; Liu and Brady, 1997Go) and the presence of intramolecular hydrogen-bonds between linked sugar units (Engelsen and Pérez, 1996Go; Ueda and Brady, 1996Go). However, carbohydrate force-fields and water models require extensive testing by comparison with experimental data, such as that provided by x-ray crystallography or NMR (Homans, 1990Go). Our previous work concentrated on studying the interaction of water with hyaluronan using aqueous molecular dynamics simulations. We noticed in our MD studies of hyaluronan tetrasaccharides that the predicted energy surface around their central linkages contained a single minima. However the ends of these molecules were predicted to be complex multi-minima surfaces, due to end effects (Almond et al., 1998aGo). Subsequently, we have demonstrated that simulations of hyaluronan tetrasaccharides in solution predict structures similar to those found in x-ray fiber diffraction. We also compared conformations predicted by these simulations with data from NMR (Almond et al., 1997Go) and hydrodynamics (Almond et al., 1998bGo). Thus, our hypothesis is that if aqueous MD simulations of carbohydrates can be compared effectively with structures proposed by x-ray crystallography, and other experimental techniques, then they could have a predictive capacity. We have noticed that most glycosaminoglycan structures refined by x-ray fiber diffraction are left-handed helices, the only exceptions being the 8-fold helices proposed for chondroitin and dermatan sulfate which are right-handed. Our aim in this paper is to understand the interaction of water with these structures. In particular the stability of intramolecular hydrogen-bonds in solution, and thus throw light onto the apparently anomalous right-handed helices.

In the present study simulations were performed on chondroitin and dermatan tetrasaccharides. However, only data for the central linkages, which do not have end-effects, are being presented. Detailed analysis of the simulations was performed to determine whether long-lived hydrogen-bonds are present in the related structures of chondroitin and dermatan, which we characterized in hyaluronan. Particular emphasis was placed on understanding the dynamics of intramolecular hydrogen-bonds and water interaction. Simulations of dermatan were performed with 4C1, 2SO, and 1C4 iduronate starting ring geometries, internal ring flexibility was allowed thereafter. We calculated the helical symmetries and axial rises for each of these structures as a function of conformation, allowing the ensemble of calculated MD structures to be compared with raw x-ray fiber diffraction data. Finally, we present our preferred solution conformations and discuss how they relate to x-ray diffraction refinements.


    Results
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
In previous studies of hyaluronan tetrasaccharides we confirmed the stability of the 4C1 chair conformation throughout 500 ps molecular dynamics (MD) simulations in solution, by calculating the Cremer-Pople ring puckering parameters (Cremer and Pople, 1975Go) as a function of time. A similar analysis of chondroitin tetrasaccharides confirmed that their constituent sugars also maintained the 4C1 chair form, throughout 500 ps aqueous molecular dynamics simulations.

We identified the presence of intramolecular hydrogen-bonds (see Materials and methods) in chondroitin tetrasaccharide simulations, Figure 1 (bottom) and compared them to our previous hyaluronan simulations, Figure 1 (top). The same hydrogen-bonds were observed across the ß(1->4) linkages of chondroitin and hyaluronan, namely: GlcA OH3...GalNAc O5, labeled (A) in Figure 1, and GalNAc NH...GlcA COO, labeled (B). Consequently, the ß(1->4) linkage of chondroitin was found to maintain a similar average conformation to hyaluronan, centered upon ({phi},{psi}) = (50°,0°). Our definitions of {phi} and {psi} are presented in Materials and methods. In contrast, the average ß(1->3) conformation for chondroitin, during a 500 ps molecular dynamics simulation in water, is ({phi},{psi}) = (50°,-30°) whereas for hyaluronan it is ({phi},{psi}) = (50°,0°).



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Fig. 1. The central linkages of the two possible tetrasaccharides of hyaluronan (top) and chondroitin (bottom). We have plotted the persistent intramolecular hydrogen-bonds as a function of time through the simulation, as described in the methods. In hyaluronan simulations we described five hydrogen-bonds, labeled A–E, and in chondroitin simulations we found four, labeled A–D.

 
Chondroitin and hyaluronan share identical ring conformation and linkage type. This implies that if chains of chondroitin and hyaluronan posses identical linkage conformation, they will also share identical helical parameters; n, the number of disaccharides per helical turn, and h, the axial rise per disaccharide. In Figure 2 the n and h values were calculated by fixing the ß(1->4) at values of {phi} and {psi} at (50°,0°) and varying {phi} and {psi} at the ß(1->3) linkage, as described in Materials and methods. Hyaluronan, as previously reported, would be predicted to prefer 3.0- to 4.0-fold helices, as compared with those for chondroitin which would be predicted to vary from 2.5 to 3.5.



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Fig. 2. The location of the glycosidic {phi} and {psi} angles, see text for definition, for the central ß(1->3) linkage of a chondroitin tetrasaccharide over a 500 ps molecular dynamics simulation in water, sampled every 1ps. The approximate area explored by a similar linkage in a hyaluronan tetrasaccharide is shown hatched. The contours detail the helices formed (in disaccharides per turn) by setting the ß(1->4) linkage at its predicted minimum energy position, ({phi},{psi}) = (50°,0°), and varying the ß(1->3) linkage. The helical parameters are calculated by the method of Miyazawa, as described.

 
Calculating the preferred n and h values by varying only a single linkage in a disaccharide repeating structure is informative, but is not rigorous. Therefore, helical parameters were calculated by varying both linkages, described in Materials and methods. However, the variation of n cannot, in this case, be easily displayed because it represents a four-dimensional surface. Known solid state conformations of chondroitin sulfate are as follows: a 2-fold helix with h = 9.8Å, a left-handed 3-fold helix with h = 9.5Å, and an 8-fold helix (either 83 or 85) with h = 9.8Å. The {phi} and {psi} values of both linkages which generate these helices, and were closest to the calculated MD solution conformation, are shown in Table I. These values have been plotted onto the calculated linkage energy contour surfaces (see methods) calculated from our MD simulations (Figure 3).


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Table I. All possible 21, 83, 85, and 32 helices that could fit the known x-ray diffraction data for chondroitin were calculated
 


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Fig. 3. Energy contours for ß(1->3) linkage (top) and ß(1->4) linkage (bottom) calculated from the molecular dynamics simulations of chondroitin as described in Materials and methods. All possible 21, 83, 85, and 32 helices which could fit the known x-ray diffraction data for chondroitin were calculated. The glycosidic angles for those helices which are closest to the molecular dynamics minima are plotted on top of the energy contours, and displayed in Table I.

 
Dermatan computer models were produced from chondroitin models by carboxyl epimerization. This change results in the conversion of ß-D-glucuronic acid to {alpha}-L-iduronic acid (IdoA). The IdoA residues were started with the 4C1 sugar ring geometry, although flexing was allowed during the simulation. Analysis of the Cremer-Pople puckering parameters confirmed that the IdoA ring was stable close to this geometry for the duration of the simulation, i.e., no major ring deformation was observed. Carboxyl epimerization induced a change in the molecular shape as compared with chondroitin, determined by our aqueous MD simulations. The geometrical arrangement of the carboxyl and OH3 groups when the IdoA residue is close to the 4C1 geometry is not sufficient to allow simultaneous hydrogen-bonds from acetamido to carboxyl and from OH3 to GalNAc ring oxygen (Figure 4a). Therefore, the molecule forms the strongest interaction, which is between carboxyl and acetamido. The average conformation of the ß(1->4) linkage was thus displaced in {psi} by some 45°, with little or no effect on {phi}, to ({phi},{psi}) = (50°,45°). At the {alpha}(1->3) linkage a slight shift in the average values of both {phi} and {psi} was observed to around ({phi},{psi}) = (45°,-45°). Fixing the {phi} and {psi} angles of a ß(1->4) linkage at (50°,45°), and varying the {phi} and {psi} values for the {alpha}(1->3) linkage allowed n and h to be calculated, Figure 4b. It is apparent that left-handed 2.5- to 4.5-fold helices dominate the minimum energy region predicted by MD.




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Fig. 4. The central linkages of the two possible tetrasaccharides of dermatan (iduronate 4C1) showing our calculated persistent intramolecular hydrogen-bonds, labeled A–D, (a) above. The persistence of these hydrogen-bonds as a function of time through the simulation, as described in the methods, are plotted (a) below. Scatter plot (b) showing the {phi} and {psi} angles sampled every 1 ps through a 500 ps simulation for the central {alpha}(1->3) linkage of a dermatan tetrasaccharide, with the iduronate residues in the 4C1 conformation. The contours show the disaccharides per turn for a helix constructed by fixing the ß(1->4) linkage at its predicted minimum energy position, ({phi},{psi}) = (50°,45°), and varying the {alpha}(1->3) linkage. The helical parameters are calculated by the method of Miyazawa, as described.

 
In solution it is predicted that IdoA exists a mixture of these ring geometries, and that they interconvert on the submicrosecond time scale (Ragazzi et al., 1986Go; Dowd et al., 1994Go). However, our simulations are apparently not long enough to overcome the energy barriers which separate conformers with different ring geometries, as observed in other MD simulations of IdoA residues for a similar total time (Mulloy et al., 1994Go). Hence, two other forms of dermatan had to be simulated, with the IdoA residues started in the 2SO and 1C4 ring geometries. Figure 5 shows the Cremer-Pople ring puckering parameters as a contour plot using data from all six dermatan tetrasaccharide simulations. Only data from the penultimate IdoA residues of tetrasaccharide was used to construct this figure.



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Fig. 5. Contour plot of the Cremer-Pople puckering parameters for internal iduronate residues in either 4C1, 2So, and 1C4 sugar ring conformations during aqueous molecular dynamics simulations of tetrasaccharides.

 
Figure 6a shows hydrogen-bonds found in a tetrasaccharide which possessed IdoA residues close to the 2SO ring geometry. In this case the hydrogen-bonds IdoA OH3...GlcNAc O5 (ring oxygen), labeled (B), and GlcNAc acetamido...IdoA carboxyl, labeled (A), can be made simultaneously across the ß(1->4) linkage, as in chondroitin. However, a hydrogen-bond involving the hydroxymethyl group, (C), is preferred over (A). Similarly, across the {alpha}(1->3) linkage both IdoA OH2...GlcNAc acetamido, labeled (D), and GlcNAc O4...IdoA O5 (ring oxygen), labeled (E), are possible. The result is that the ß(1->4) linkage is shifted in {psi} by 30° and the {alpha}(1->3) linkage is unchanged with respect to the hyaluronan ß(1->3) linkage. Using this 2SO IdoA form of dermatan, n and h values were calculated by fixing the {alpha}(1->3) linkage at ({phi},{psi}) = (50°,0°) and varying the ß(1->4) linkage (Figure 6b). The helices explored by the solvated MD simulations correspond to two-handed and left-handed 3-fold helices of 7.9 < h < 9.4(Å).




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Fig. 6. The central linkages of the two possible tetrasaccharides of dermatan (iduronate 2SO) showing our calculated persistent intramolecular hydrogen-bonds, labeled A-F, (a) above. The persistence of these hydrogen-bonds as a function of time through the simulation, as described in the methods, are plotted (a) below. Scatter plot (b) showing the {phi} and {psi} angles sampled every 1 ps through a 500 ps simulation for the central ß(1->4) linkage of a dermatan tetrasaccharide, with the iduronate residues in the 2SO conformation. The contours show the disaccharides per turn for a helix constructed by fixing the {alpha}(1->3) linkage at its predicted minimum energy position, ({phi},{psi}) = (50°,0°), and varying the ß(1->4) linkage. The helical parameters are calculated by the method of Miyazawa, as described.

 
The persistence of hydrogen-bonds reduces dramatically in dermatan tetrasaccharides containing IdoA residues close to the 1C4 geometry, compared with tetrasaccharide which possessed IdoA residues close to the 2SO geometry, (Figure 7a). In particular there are no persistent intramolecular hydrogen-bonds bridging adjacent monosaccharides. Figure 7b shows the n and h values calculated by restricting the {alpha}(1->3) linkage to ({phi},{psi}) = (50°,0°) and varying the ß(1->4) linkage. The predominant predicted conformations are left-handed 4.0- to 6.0-fold helices, with pitches in the range 8.8 < h < 9.0 (Å).




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Fig. 7. The central linkages of the two possible tetrasaccharides of dermatan (iduronate 1C4) showing our calculated persistent intramolecular hydrogen-bonds, labeled A-F, (a) above. The persistence of these hydrogen-bonds as a function of time through the simulation, as described in the methods, are plotted (a) below. Scatter plot (b) showing the {phi} and {psi} angles sampled every 1 ps through a 500 ps simulation for the central {alpha}(1->3) linkage of a dermatan tetrasaccharide, with the iduronate residues in the 1C4 conformation. The contours show the disaccharides per turn for a helix constructed by fixing the {alpha}(1->3) linkage at its predicted minimum energy position, ({phi},{psi}) = (50°,0°), and varying the ß(1->4) linkage. The helical parameters are calculated by the method of Miyazawa, as described.

 

    Discussion
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Chondroitin differs from hyaluronan by the epimerization of a single hydroxyl group at the 4-position of the hexosamine residue. This significantly changes the environment around the ß(1->3) linkage. Our simulations predict that in chondroitin the hexosamine OH4 does not form an efficient direct intramolecular hydrogen-bond, as it can in hyaluronan, labeled (D) in Figure 1. Instead, these groups are stabilized by the presence of intervening water molecules. Consequently, the dynamic environment of the hydroxymethyl group in chondroitin is affected in a way that disfavors an intramolecular hydrogen-bond, labeled (E), involving the hydroxymethyl group, which was present in hyaluronan simulations. The predicted lack of a hydrogen-bond involving OH4 across the ß(1->3) linkage of chondroitin was observed to allow the acetamido to relax closer to its preferred trans (H2-C2-H-N) arrangement, which reduces the persistence of hydrogen-bonds (A) and (C) (see Figure 1), in the chondroitin structure as compared to the hyaluronan structure. This results in the differences in conformation at the ß(1->3) linkage observed for chondroitin and hyaluronan. However, these changes do not affect the GlcA OH3...hexosamine ring oxygen hydrogen-bond, which can be formed in both chondroitin and hyaluronan, and hence the ß(1->4) linkage is similar in the two cases.

Comparing hyaluronan with chondroitin, the overall predicted effect of hexosamine OH4 epimerization is to change the average conformation from approximately left-handed 4-fold to 3-fold helices. This would appear to be reflected in previous x-ray fiber diffraction refinements. Hyaluronan prefers 43 helices (Mitra et al., 1983aGo) when crystallized with weakly perturbing monovalent sodium or potassium ions, and under neutral pH conditions. Chondroitin sulfate, on the other hand, has not been observed to crystallize into any 4-fold structures. However, both chondroitin-4-sulfate and chondroitin-6-sulfate have been refined into a 32 packing arrangement in the presence of sodium ions (Millane et al., 1983Go). A 2-fold helix has been observed in chondroitin-4-sulfate (Cael et al., 1978Go), but this was in the presence of calcium, which can be seen to be coordinated between carboxyl and sulfate moieties in the refinement, and is therefore dominated by the effect of the highly charged calcium ion. Similarly, a 2-fold helix was observed with chondroitin-6-sulfate at low pH, a situation that cannot be compared to the conditions under which we performed our simulations. As far as we are aware, the 8-fold helix observed in chondroitin-6-sulfate has never been accurately refined (Arnott et al., 1973Go), although Arnott et al. originally represented the structure as an 85 helix. Subsequent reviews have come to represent the structure as an 83 helix on the basis of later refinements performed on dermatan sulfate (Ernst et al., 1995Go).

Based on our data, and the x-ray fiber diffraction literature, it would appear that at neutral pH and in the presence of sodium it is the satisfaction of intramolecular hydrogen-bonds that dominates the conformation of chondroitin sulfate, rather than the distribution of sulfation. In fact, none of the possible targets for sulfation in chondroitin have been observed to be involved in intramolecular hydrogen-bonds, supporting our claim. Conversely, in the hyaluronan we predict that these groupings do play important roles, involving themselves in intramolecular hydrogen-bonds, as shown in Figure 1. Hyaluronan, in contrast to chondroitin, has not been found to be sulfated.

The presence of strong intra-molecular hydrogen-bonds in chondroitin sulfate has experimental backing, in the form of periodate oxidation kinetic measurements (Scott and Tigwell, 1978Go). In Figure 8 possible 2-, 3-, and 8-fold helices have been constructed which are closest to the chondroitin MD energy minima. The dihedral angles applied to the linkages are detailed in Table I. In each diagram the structural intra-molecular hydrogen-bonds, GalNAc NH...GlcA COO and GlcA O2...GalNAc O7, have been labeled by (A) and (B) respectively. Both hydrogen-bonds, (A) and (B), can be observed in the 21, 85, and 32 structures. However, in the right-handed 83 structure hydrogen-bond (B) cannot form, and this is labeled by (X).



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Fig. 8. Different calculated helices for chondroitin, showing intra-molecular hydrogen-bonds (dashed line). R8, 83 right-handed helix of chondroitin-6-sulfate; 2,– 21 helix of chondroitin-4-sulfate; L8, right-handed 83 helix of chondroitin-6-sulfate; and L3, left-handed 32 helix of chondroitin. The two most common hydrogen-bonds are labeled (A) and (B). Label (X) shows the absence of hydrogen-bond (B) in our calculated 83 helix.

 
Eight-fold helices of dermatan sulfate have been characterized by x-ray fiber diffraction in the presence of sodium (Mitra et al., 1983bGo). In these studies the chains were refined using IdoA residues with 4C1 ring geometry. The only alternative at that time was considered to be the 1C4 conformation. This structure was dismissed on the basis of its inability to provide the required axial-rise, recently confirmed by Venkataraman et al. (1994)Go, also in agreement with our MD data. Right- and left-handed helices of chains with either 4C1 or 1C4 IdoA sugars were considered in the refinement of the 8-fold x-ray diffraction pattern. The author who performed the original refinements commentated that the right-handed 83 helix provided the best packing arrangement, even though it possessed fewer intramolecular hydrogen-bonds between sugar residues than the 85 alternative. However, NMR studies on similar fibers in the solid-state concluded that the "[iduronate] ring conformation was a distorted version of the 1C4 family" (Winter et al., 1986Go). Models containing 2SO IdoA conformers were not considered in this early work, they were suggested later to consolidate NMR observations (Casu, 1986Go). Ragazzi et al. (1990)Go proved that such models could, in principle, satisfy the symmetry and helical rise criteria found by x-ray diffraction.

Our simulations suggest that dermatan structures containing IdoA residues with a 4C1 ring geometry can maintain strong interactions between the carboxyl and adjacent acetamido moieties. This interaction is predicted to occur at the expense of the hydrogen-bond between OH3 on IdoA and the ring oxygen on hexosamine, resulting in the observed shift of its ß(1->4) linkage with respect to chondroitin. However, the conformation of the acetamido is such that interaction with IdoA OH2 perturbs the {alpha}(1->3) linkage and allows the hydrogen-bond GalNAc OH4...IdoA O5 (ring oxygen) to exist simultaneously. The preferred helices sampled at the predicted MD energy minima (Figure 4b), with IdoA in a 4C1 conformation, are all left handed (2.5- to 4.5-fold) in contrast to the 8-fold dermatan fiber diffraction refinement, which is right-handed. However, these models have been rejected by x-ray refinement on the basis of packing considerations. Accepting this, our molecular dynamics studies would suggest a left-handed 85 helical conformation containing 2SO IdoA sugars. In this conformation the chains can maintain intramolecular hydrogen-bonds and at the same time produce the required axial-rise. This model would agree with solid state and current solution NMR data (Rao et al., 1995Go). Taken together these observations suggest that the 8-fold dermatan x-ray diffraction data should be re-refined with inclusion of left-handed 2SO IdoA models. Based on our MD simulations, we can depict minimum energy models for helices containing the three IdoA forms (Figure 9). The model containing IdoA residues with 1C4 ring geometry has a sinuous contracted structure. Such structures could be present in solution, but the process of drying and fiber stretching may discriminate against them. We have compared a skew boat model (2SO) with 85 symmetry, lying close to the minimum predicted by MD, with the literature model of the 83 helix. This highlights a difference in intramolecular hydrogen-bonds. Based on our simulations, we also conclude that chains containing IdoA with either 4C1 or 2SO ring geometry can be used as starting models for the observed 2-fold and 3-fold diffraction patterns of dermatan fibers (Nieduszynski, 1985Go, and references therein). Similarly, we suggest that in chondroitin fibers an 85 helix is more energetically favorable than an 83 helix, and in the absence of other data the former structure should be assumed. If these conclusions are true, then all known x-ray diffraction structures of glycosaminoglycans would be extended 2-fold or left-handed conformations which have optimized intramolecular hydrogen-bonds.



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Fig. 9. Our calculated minimum energy structure for dermatan containing 1C4 iduronate residues (a), which is contracted. Our calculated left-handed 8-fold dermatan helix containing 2SO residues (b), which satisfies the x-ray diffraction observations. The original right-handed 8-fold x-ray fiber diffraction refinement of dermatan sulfate (Mitra et al., 1983bGo) containing 4C1 iduronate (c).

 
Data presented here, together with the previous MD observations on hyaluronan suggest that with explicit inclusion of water molecules, glycosaminoglycans can be modeled with increasing confidence. Although we have not included sulfation or cations in our models, the results appear to agree with the conformations predicted by x-ray diffraction performed on fibers complexed with monovalent ions. The work presented here provides a first step towards understanding the contribution of sulfate and cations on the conformation of these molecules, which may require their explicit inclusion. Effective molecular modeling of chondroitin and dermatan provide the basis for examining more complex situations. In particular, heparin and heparan sulfate contain complex block co-polymeric structures with variable uronic acid type (Lindahl et al., 1998Go). These molecules are found in complex associations with numerous proteins (Ornitz et al., 1995Go; Faham et al., 1996Go). Our work provides the foundation to model these structures and their interactions with proteins more confidently.


    Materials and methods
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Molecular dynamics
Molecular dynamics was performed with the explicit inclusion of water molecules into the simulation using CHARMM25 (Brooks et al., 1983Go) using version 22 parameters with extensions for carbohydrates. Explicit consideration of the exo-anomeric effect was included in the force-field. Partial charges were calculated with Gaussian 98 (Frisch et al., 1998Go) using the HF/6–31G* basis set for N-acetylated sugars and HF/6–31G** for carboxylated sugars. Each of the different iduronate (IdoA) ring conformers considered (4C1, 2SO, 1C4) was assigned a specific set of partial charges.

Molecular dynamics integration was carried out using the leap-frog formulation (Hockney, 1970Go) of the Verlet algorithm (Verlet, 1967Go), and hydrogen covalent bond length were kept constant using the SHAKE procedure (van Gunsteren and Berendsen, 1977Go). An integration step size of 1 fs was used to provide precise trajectories. No explicit hydrogen-bonding function was used in the simulations, as it is assumed that they are well represented by the partial atom charges and van der Waals parameters (Brady and Schmidt, 1993Go).

Solvated simulations used 32 Å water boxes, filled with 1000 TIP3P previously equilibrated water molecules (Jorgensen et al., 1983Go). The initial configuration was achieved by minimization using adopted basis Newton-Raphson approach, heating for 3 ps at a rate of 100K ps–1, followed by 50 ps of diabatic equilibration at 300K. Subsequently 500 ps of adiabatic dynamics was performed. Coordinates were written every 0.05 ps, and the nonbonded lists were updated using the grid search cubing algorithm at a heuristic frequency. Edge effects were overcome by implementing cubic periodic boundary conditions, and the electrostatics were reduced to zero over the range 8–12 Å using the shifting function.

Calculation of dihedral angles and hydrogen-bonds
The linkage conformation was represented by dihedral angles {phi} (H1-C1-Ox-Cx) and {psi} (C1-Ox-Cx-Hx) defined by the hydrogen atoms. Hydrogen-bonds were calculated as in our previous work (Almond et al., 1997Go, 1998a). Our definition of a hydrogen-bond is identical to that used by other authors who have analyzed carbohydrate simulations (Brady and Schmidt, 1993Go), the distance of D (hydrogen donor) to A (hydrogen acceptor) is less than 3.5 Å, and the angle D-A...A is less than 60°. Hydrogen-bonds were then calculated between all relevant groups during each simulation. The data is grouped into 4 ps intervals, and a persistent hydrogen-bond is counted if it is present for 50% of the time over this period. Any groups which have no persistence of hydrogen-bonding during any of these time periods are ignored.

Calculation of n and h parameters
Calculation of the helical fold (n) as a function of polysaccharide linkage conformation was based on a general method described in the literature (Miyazawa, 1961Go; Sugeta and Miyazawa, 1967Go). In this method the polymer is built up from a series of virtual vectors which describe the smallest repeating unit (a disaccharide in this case). Therefore, short oligomeric sections with specific ({phi}1->3, {psi}1->3) and ({phi}1->4, {psi}1->4) angles at the two linkages were constructed. The positions of the glycosidic oxygen atoms were then extracted and used to calculate n and h for each conformation. Further details are provided in our previous paper (Almond et al., 1998bGo). Contour plots were calculated by varying a single linkage while constraining the other to a particular conformation (Figures 2, 4b, 6b, 7b). Dihedral angles relating to specific x-ray diffraction data were calculated by varying all linkages and selecting those conformations which satisfied the helical parameters. The dihedrals which were closest to our calculated solution MD energy for that particular structure were then selected, and tabulated. Three-dimensional structures shown in Figures 8 and 9 were rendered with the package Raster3D (Merritt and Bacon, 1997Go).

Calculation of energy contours
Pairs of dihedral angles ({phi},{psi}) were extracted as a function of time for each of the linkages. The conformational space was then split into a grid at 5° intervals, and the probability of pairs of dihedral angles occurring at different grid points calculated. If it is assumed that the space has been efficiently sampled, and that the energy states are nondegenerate, then the energy at each point is proportional to the logarithm of the probability. Thus, the energy was calculated at each point and negated, and then these were rescaled such that the lowest energy corresponded to the zero energy. This data was used to construct contour plots in Figure 3. An identical approach was used to calculate the Cremer-Pople contour surface of Figure 5.


    Acknowledgments
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
Financial support for this work was provided by a Wellcome Trust prize fellowship, grant reference number 052055.


    Abbreviations
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
GlcNAc, N-acetyl-glucosamine; GalNAc: N-acetyl-galactosamine; GlcA, glucuronic acid; IdoA, iduronic acid; MD, molecular dynamics; NMR, nuclear magnetic resonance.


    Footnotes
 
1 To whom correspondence should be addressed at: Department of Chemistry, Carlsberg Research Centre, Gamle Carlsberg Vej 10, DK-2500, Valby, Copenhagen, Denmark Back


    References
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 Acknowledgments
 Abbreviations
 References
 
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