Predicting the molecular shape of polysaccharides from dynamic interactions with water

Andrew Almond1,2 and John K. Sheehan3

2 Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU United Kingdom
3 Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA

Received on July 29, 2002; revised on October 30, 2002; accepted on November 21, 2002


    Abstract
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 References
 
How simple monosaccharides, once polymerized, become the basis for structural materials remains a mystery. A framework is developed to investigate the role of water in the emergence of dynamic structure in polysaccharides, using the important ß(1->4) linkage as an example. This linkage is studied within decasaccharide fragments of cellulose, chitin, mannan, xylan, and hyaluronan, using molecular simulations in the presence of explicit water solvent. Although cellulose, mannan, chitin, and xylan are chemically similar, their intramolecular hydrogen-bond dynamics and interaction with water are predicted to differ. Cellulose, mannan, and chitin favor relatively static intramolecular hydrogen bonds, xylan prefers dynamic water bridges, and multiple water configurations are predicted at the ß(1->4) linkages of hyaluronan. With such a variety of predicted dynamics, the hypothesis that the ß(1->4) linkage is stabilized by intramolecular hydrogen bonds was rejected. Instead, it is proposed that favored molecular configurations are consistent with maximum rotamer and water degrees of freedom, explaining observations made previously by X-ray diffraction. Furthermore, polysaccharides predicted to be conformationally restricted in simulations (cellulose, chitin, and mannan) prefer the solid state in reality, even as oligosaccharides. Those predicted to be more flexible (xylan and hyaluronan) are known to be soluble, even as high polymers. Therefore an intriguing correlation between chemical composition, water organization, polymer properties, and biological function is proposed.

Key words: cellulose / hyaluronan / polysaccharide / water / xylan


    Introduction
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 References
 
Polysaccharides are the most abundant macromolecules in the living world (Aspinall, 1985Go), and constitute a major store of carbon, nitrogen, and photosynthetic potential energy within the Earth's dynamic ecosystem (Haigler et al., 2001Go; Karnezis et al., 2000Go). They are employed in diverse roles, as structural molecules in plants (cellulose) and arthropods (chitin) or as dynamic lubricating components of the mammalian extracellular matrix (hyaluronan, proteoglycans) and cell surface coatings (heparan sulfate proteoglycans) on which protein recognition and cell–cell adhesion can occur (Sugiyama and Imai, 1999Go; Muzzarelli and Muzzarelli, 1998Go; Lee and Spicer, 2000Go; Iozzo, 1998Go; Lyon and Gallagher, 1998Go). A molecular appreciation of how these molecules perform their various functions is potentially forthcoming from studies of three-dimensional structure and dynamics. The current understanding of polysaccharide shape and form is largely based on models constructed from in vacuo calculations of internal energy (molecular modeling), X-ray diffraction, and nuclear magnetic resonance (Duus et al., 2000Go). A compendium of this work has recently been brought together and summarized (Rao et al., 1998Go). Such information has allowed a reasonable representation of the average structure of polysaccharides, but it has not explained why some polysaccharides are the basis of highly insoluble crystalline complexes whereas others, only subtly different in chemical structure, form gums, gels, and viscoelastic solutions. For example, in the case of cellulose, it is completely obscure how one of the most soluble biomolecules on the planet (glucose) can, after knitting some half a dozen residues together, become the basis of the most insoluble (Tonnessen and Ellefsen, 1971Go). It is suggested here how these properties are emergent from their interactions with water.

Although adiabatic in vacuo energy calculations have played an important role in providing intuition about the likely conformations of polysaccharides, included in this approach is the smearing out of water into a smooth fluid of constant dielectric. The assumption that molecular water plays a minor role in the emergence of the shape and dynamics of such polymers is therefore implicit. The main impetus for their use was to allow predictions to be made with modest computational resources. However, during the development of molecular mechanics simulations, it was recognized that the conformational structure and dynamics of biopolymers was strongly influenced by the presence of water (Franks, 1983Go; Brady, 1990Go). This resulted in important simulations of carbohydrates with explicit water when computing resources were extremely limited. The first simulations included glucose (Brady, 1989Go), the sugar alcohols sorbitol and mannitol (Grigera, 1988Go), and {alpha}-cyclodextrin (Koehler et al., 1988Go).

Advances in computational power are removing the need to make the severe approximations associated with treating water as a continuum. Supercomputers can now perform simulations of biomolecules with explicit solvent out to the microsecond timescale (Duan and Kollman, 1998Go), to explore kinetic phenomena, such as protein folding. However, relatively extensive simulations of polysaccharide fragments in the presence of water molecules are possible without the need for supercomputers. The results of such simulations are confirming that water has important effects on the nature of carbohydrate dynamics, which are more substantial than simply introducing an increased dielectric or viscosity (Kirschner and Woods, 2001Go). These studies give considerable insight into why relatively small changes in polysaccharide chemical structure can result in large changes in their physical properties, which go far beyond predictions based on simple in vacuo modeling.

Recently, we reported the results of long simulations on a range of oligosaccharides of hyaluronan, a polymer of alternating ß(1->3) and ß(1->4) linkages (Almond et al., 2000Go), in the presence of explicit water molecules. These simulations were carefully compared against X-ray diffraction, nuclear magnetic resonance, circular dichroism, and hydrodynamic data (Almond et al., 1988aGo,bGo). From the large agreement between simulation and experiment it was concluded that simulations can provide new insights into the unexplored microscopic dynamics of the hyaluronan polymer. Important microscopic information was forthcoming from these studies, providing a new understanding of both the physiochemical and biological properties of hyaluronan. Contrary to previous hypotheses of hyaluronan secondary structure (Atkins et al., 1980Go), the molecule was predicted to have intrinsic flexibility at the ß(1->4) linkage. This is exemplified in Figure 1a, showing glycosidic data from the four ß(1->4) linkages in the decasaccharide structure simulated in water for 5 ns, overlaid on the same plot (see Materials and methods for angular definitions). Specific conformations at the linkage were occupied for periods on the nanosecond timescale, whereas transitions occurred rapidly on the subnanosecond timescale (Figure 1b). The predicted stability and instability of particular conformations, the transition time between them, and the resulting effect on structure were in no way intuitive and raised questions about the behavior of the ß(1->4) linkage in other carbohydrate polymers.



View larger version (32K):
[in this window]
[in a new window]
 
Fig. 1. The chemical structure of hyaluronan, showing the repeating disaccharide, and the hydrogen bonds that have been proposed to stabilize the ß(1->4) linkage (Atkins et al., 1980Go). (a) The glycosidic angles (see Materials and methods for definitions) predicted from a simulation of a hyaluronan decasaccharide (Almond et al., 2000Go). The data for four linkages has been overlaid onto the same plot. (b) A plot of the {Psi}-angle for a single ß(1->4) linkage as a function of time from an aqueous simulation of hyaluronan.

 
In this article the consequences of some of these findings for other ß(1->4) linkages found in cellulose, mannan, chitin, and ß(1->4)-linked xylan are explored. It is predicted that apparently minor modifications of side groups and hydroxyl positions result in effects that would not be expected from nonaqueous models and are curiously mirrored by previous experimental observations. Important new insights into the role of water in organizing polysaccharide structure are emergent from these studies, which point the way toward creating a new dynamic language for visualizing the effects of water on both oligosaccharide and polysaccharide structure.


    Results
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 References
 
The unexpected rigidity of cellulose in aqueous solution
Dynamic simulations of length 5 ns containing explicit water molecules were performed on decasaccharides of cellulose, mannan, chitin, and ß(1->4)-linked xylan (see Materials and methods). They were examined in a similar way to that described previously for a hyaluronan decasaccharide (Almond et al., 2000Go). Glycosidic torsion angles for every linkage were extracted at 100-fs intervals during each simulation, using definitions described in Materials and methods. In Figure 2 the torsion angles for all nine linkages have been overlaid onto individual plots for cellulose, xylan, mannan, and chitin. As exemplified by hyaluronan previously (Figure 1), the ß(1->4) linkage can occupy relatively large areas of its conformational space. However, comparison of the simulation of cellulose against that for hyaluronan produced an immediately interesting prediction; namely, that the glycosidic linkages in cellulose are more tightly restricted than the hyaluronan equivalent (Figure 2a) even though the cellulose linkage is paradoxically less sterically obstructed. Such an observation is preliminary evidence that forces other than steric repulsion are at work around the glycosidic linkages, perhaps involving water molecules.



View larger version (35K):
[in this window]
[in a new window]
 
Fig. 2. The chemical structures and predicted glycosidic populations for the ß(1->4) linkages of (a) cellulose, (b) xylan, (c) mannan, and (d) chitin. The data were extracted from 5-ns molecular dynamics simulations with explicit water molecules. See Materials and methods for angular definitions.

 
As a simple parameter for visualizing linkage dynamics and water interaction, intramolecular hydrogen bonds were documented at regular intervals throughout the cellulose simulation. Their definition was initially based on angle and distance criteria (see Materials and methods). As in a previous article (Almond et al., 2000Go), the number of observed hydrogen-bond pairs was calculated as a function of time (Figure 3a). This graph was used, as previously, to ensure that adequate conformational sampling had taken place. After a period as short as 500 ps, all of the persistent intramolecular hydrogen-bonds had been observed (lower part of the graph); implying that these conformations were highly sampled during the simulation. Furthermore, few new interactions were seen after a period of 2 ns had elapsed, indicating that a large percentage of conformational space had been sampled during this period and confirming that simulations of length 5 ns were adequate to ensure statistical sampling of the major conformers. This was also evident from the observation that each of the internal linkages in the decasaccharide populated space in an identical way. If this were not true, then inadequate conformational sampling would be suspected. Similar checks were made for all of the decasaccharide simulations, with similar results, but the graphs are not shown.



View larger version (22K):
[in this window]
[in a new window]
 
Fig. 3. Intramolecular hydrogen bonds found in a cellulose decasaccharide from a 5-ns simulation in the presence of explicit water molecules. (a) Shows all of the hydrogen bonds numbered in order of observation, irrespective of the type of interaction. (b) Shows the important interactions (A–C) found across the ß(1->4) linkages of cellulose. (c) Shows the presence of the interactions detailed in (b) at each of the linkages in the decasaccharide and the molecular length as a function of time. Marked over this is the molecular length which would be predicted if the molecule took up a conformation as in the cellulose-I crystal.

 
The nature of these hydrogen bonds can be elucidated by separating them into categories. In the case of cellulose, three major intramolecular hydrogen-bonding interactions were observed, and these are labeled A, B, and C in Figure 3b. Their presence during the simulation, at each linkage, is detailed in Figure 3c. Hydrogen bond A corresponds to the localization of OH3 with respect to O5 and is predicted to be a particularly persistent interaction in the cellulose structure as seen in Figure 3c. The other two interactions involve the hydroxymethyl moiety; B represents the interaction from OH3 to O6, and C represents the interaction from OH6 to O3.

Observation of the molecular length as a function of time permits a visualization of the overall polymer dynamics. This parameter is documented from the simulation of a cellulose decasaccharide in Figure 3c. On this figure the predicted length for a decasaccharide based on the axial rise observed in the cellulose I crystal (Gardner and Blackwell, 1974Go) has been marked (5.15 nm) and is close to the maximum length obtainable for cellulose. The predicted dynamic length stayed close to this value for the majority of the cellulose simulation, although excursions to more contracted conformations (~4.4 nm) were observed ephemerally. These excursions correspond to unusual conformations, and presumably water structure, at one or more of the polymer linkages, which last for only a few picoseconds. Thus the emergent average polymer conformation is highly extended and very close to that observed in crystal structures.

Chitin and mannan are cellulose-like; xylan is not
Use of the analysis strategies already applied to hyaluronan and cellulose allows comparison to be extended to a larger variety of polysaccharides. The most frequently observed conformations and extent of glycosidic motion can be compared between hyaluronan, cellulose, xylan, chitin, and mannan using the ({phi}, {Psi}) plots of Figures 1a and 2. The similarity of cellulose, chitin, and mannan is noticeable, but in xylan there is a distinct difference. Also, the hyaluronan data highlights that different polymers have specific and different preferences around the ß(1->4) linkage. Hence the structure and dynamics of these polymers is predicted to be sequence specific.

The occurrence of intramolecular hydrogen-bonds at each linkage during simulation are shown in Figures 3c and 4 for cellulose, chitin, mannan, xylan, and the ß(1->4) linkage of hyaluronan. It can be seen that cellulose, chitin, and mannan share similar intramolecular hydrogen-bond dynamics, coincident with their similar glycosidic conformational preference. In all of these structures the interaction between OH3 and O5 is present for greater than 80% of the time. However, in the xylan structure this interaction is almost completely absent and instead moves away into another region. The consequence of this can be seen in Figure 4a, where the predicted molecular length for xylan has been plotted as a function of time. Also on this diagram the predicted length of a decasaccharide, based on the xylan left-handed three-fold X-ray fiber diffraction structure (Nieduszynski and Marchessault, 1972Go), has been marked (4.95 nm) as compared with that for the cellulose structure. For mannan and chitin the predicted length variation is shown in Figures 4b and 4c, together with the values observed in crystal fibers of mannan-I/II (Atkins et al., 1988Go) and {alpha}/ß-chitin (Gardner and Blackwell, 1975Go), again in good agreement. Similarly for hyaluronan, crystal structures are known (Atkins et al., 1972Go; Winter et al., 1975Go; Sheehan and Atkins, 1983Go) that would predict lengths of 4.9 nm and 4.2 nm as upper and lower limits, but 4.75 nm is most frequently observed (Figure 4d). This is, intriguingly, in excellent agreement with the simulated dynamics.



View larger version (36K):
[in this window]
[in a new window]
 
Fig. 4. Intramolecular hydrogen bonds and molecular length as a function of time in 5-ns molecular dynamics simulations of decasaccharides with explicit water molecules. (a) Xylan and the interaction is OH3–O5. (b) Mannan, the interactions are as in cellulose (see Figure 3b). (c) Chitin, the interactions are as in cellulose (see Figure 3b). (d) Hyaluronan, interactions are described in Almond et al. (2000)Go. Dotted lines denote length predictions based on previous X-ray fiber diffraction studies; xylan 3-fold symmetry, mannan I/II, chitin {alpha}/ß and hyaluronan in K+, Na+, and Ca2+ salts and a variety of pH values (see text).

 
Observing the subtle but dominating effects of water
Comparison of the dynamics of several different ß(1->4) linkages suggested that the hydrogen bond between OH3 and O5 may not be a criterion for structuring but simply consistent with it. To examine this idea, the hydrogen bond in question was examined in more detail. The distance between O3 and O5 and the angle between O3, OH3, and O5 was extracted across one of the linkages and is plotted in Figure 5a and b for both cellulose and xylan because the notion of a hydrogen bond is related to distance and angular criteria. In cellulose the region around the distance 0.28 nm and angle 150° is highly populated and corresponds to what was originally called an intramolecular hydrogen bond. However, in xylan the system bifurcates. Two new regions are populated at 0.41 nm, 110° and 0.42 nm, 20°. They correspond to water-bridged linkages and differ simply by rotation of the OH3 hydroxyl group, a rotation not favored in the cellulose structure. The dynamic water structure in xylan results in a shift in the glycosidic conformation to ({phi}, {Psi})=(50°, 50°), as compared with cellulose conformation at (60°, 0°) (Figure 5c). On this diagram iso-lines are drawn that correspond to linkage geometries that produce exact two- and threefold helices for the polymers. It can be seen that the cellulose linkage localizes to the twofold iso-line and xylan is close to the threefold iso-line. Typical predicted conformations and local water structure for the linkages of cellulose and xylan are shown in Figure 6. This is in exact agreement with the known crystal structures. Thus, differences between computer predictions are reflected in solid experimental data.



View larger version (26K):
[in this window]
[in a new window]
 
Fig. 5. Predictions for the most populated conformations of (a) cellulose and (b) xylan. On these plots the distance O3 to O5 is plotted against the angle O3, OH3, O5. (c) Shows the effect of changes in water structuring on the predicted linkage conformation using population contour maps. Marked on this plot are the iso-lines where linkage geometries result in particular crystal morphologies for the polymer.

 
Plots of the distance between O3 and O5 and the angle between O3, OH3, and O5 for chitin and mannan show very similar behavior to cellulose; compare Figure 7a and b with Figure 5a. Again, the region around distance 0.28 nm and angle 150° is highly populated, indicating stability of the hydrogen bond between OH3 and O5. The emergent preferred structures for chitin and mannan are shown in the disaccharides of Figure 7c and d. Certainly, as exemplified by their variation of molecular length with time (Figures 3c, 4b, and 4c) these molecules appear to be very constrained, remarkably rigid, and almost fully elongated.



View larger version (40K):
[in this window]
[in a new window]
 
Fig. 7. Identifying the most populated regions for the linkages of (a) mannan and (b) chitin. On these plots the distance O3 to O5 is plotted against the angle O3, OH3, O5 and can be compared against cellulose and xylan in Figure 5. The predicted conformations of (c) mannan and (d) chitin, which are cellulose-like.

 


View larger version (31K):
[in this window]
[in a new window]
 
Fig. 6. Stereo views of the predicted favorable conformations for cellulose and xylan. (top) Shows the direct hydrogen bond between OH3 and O5 predicted in cellulose and free water structure bridging the O6 and O3 moieties. (bottom) Shows the most highly populated water-bridged structure observed in the xylan polymer, allowing free rotation of OH3, and thus differing from cellulose.

 
So why is the OH3–O5 hydrogen bond highly favored in some cases of the ß(1->4) linkages and not in others? In the case of hyaluronan, the cellulose-type interaction is certainly present but not dominant. It is the interaction of the amide proton with carboxyl moiety that dominates, and thus the linkage is partially drawn toward another conformation, not sampled in cellulose. In this case there are two water environments to be considered, one at either side of the linkage. Plotting the {Psi} torsion angle against the angle between O3, OH3, and O5 for a particular ß(1->4) linkage demonstrates these two major conformations and their relative populations (Figure 8). One is similar to that found in cellulose and corresponds to {Psi}=0°. The other is where a favorable interaction between carboxyl and acetamido occurs and involves water bridges. In this conformation the O3 group rotates into bulk water. Again consideration of the molecular length as a function of time (Figure 4d) reveals how this microscopic instability of interactions carries through to polymer dynamics. As compared with cellulose (Figure 3c) and even xylan (Figure 4a) there are significant fluctuations in the molecular length predicted for hyaluronan.



View larger version (70K):
[in this window]
[in a new window]
 
Fig. 8. Identifying the conformational attractors in hyaluronan. Two regions are observed with differing linkage geometry. On this plot the distance O3 to O5 is plotted against the angle O3, OH3, O5 and can be compared against cellulose and xylan in Figure 5 and mannan and chitin in Figure 7. Exchange between them results in polymer chain dynamics, possibly leading to its high solubility.

 

    Discussion
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 References
 
Water interactions at linkages dominate the dynamics
Three distinctively different kinds of dynamic behavior for the ß(1->4) linkage have been highlighted in five different polymers. Based on these observations, relationships between dynamic conformation and primary chemical structure are evident. First, it is predicted that modification of position C2 of glucose has little effect on the dynamics as compared with modification at position C5. Second, the data indicate there is something special relating to the substitution at this position that has not previously excited attention. The xylan and hyaluronan data also undermine the idea that the O3–O5 hydrogen bond (A in Figure 3b), is in some way special or strongly stabilizing at ß(1->4) linkages. Therefore, an alternative explanation for the presence and absence of hydrogen bonds than those typically offered must be sought.

That there is a very high degree of restriction predicted by the simulations at the linkages of cellulose can be exemplified by comparison with molecular length predictions based on steric hindrance alone. In Figure 9 the distribution of molecular lengths for cellulose has been plotted from the simulation as compared with distribution of molecular lengths predicted by allowing the linkages to explore all of the sterically accessible ß(1->4) space with equal probability. Thus in water there appears to be a strong force acting to elongate the molecule. If there is, how is water implicated in the emergence of such a force? It is also remarkable that the predicted dynamic structure for the oligosaccharides in water is so similar to that observed for the high polymer fibers in X-ray diffraction studies (Gardner and Blackwell, 1974Go); the consequences of this will be discussed later.



View larger version (63K):
[in this window]
[in a new window]
 
Fig. 9. Binned molecular lengths for random configurations of cellulose generated by exploring the whole sterically allowable space with equal probability (see Materials and methods). The most frequently observed length is distant from the theoretical maximum extension, as anticipated. Binned molecular lengths for cellulose, xylan, and hyaluronanextracted from aqueous molecular dynamics simulations are shown for comparison.

 
It would not be expected a priori that the polymers, such as cellulose, would intrinsically prefer such extended conformations, so why are they observed? Detailed comparison of the cellulose and xylan simulations appears to give a clue. Absence of the hydroxymethyl moiety in xylan promotes a shift in the preferred glycosidic linkage population from conformation in which the hydrogen bond (A in Figure 3b) is present, as found in cellulose, to conformational states involving water bridges (described for xylan in Figure 5b). Thus the average emergent conformation in xylan is a left-handed threefold helix just as found in the hydrated fiber X-ray diffraction structure (Nieduszynski and Marchessault, 1972Go). This has been something of a mystery and has previously been commented on by Rao et al. (1998)Go in their book on carbohydrate conformation. We quote: "In terms of intra-molecular forces, it is difficult to understand why (1->4)-xylan favors a threefold screw symmetry instead of twofold as in cellulose. It is tempting to attribute the preference to interactions between chains and water molecules in the lattice (since there is evidence of at least one water molecule per xylose residue in the unit cell)." From these simulations it is apparent that water interactions may underlie these changes in conformation and that qualitatively at least the simulations mirror the experimental observations. However, a significant challenge remains: If one now assumes that the hydroxymethyl group is implicated in defining the restricted cellulose conformation, as opposed to xylan, how is this to be explained at the microscopic level?

A dynamic description of polysaccharide–water interaction
To offer a reductive explanation for the data, the nature of interactions of molecular water with the linkage must be reconsidered and compared with intramolecular hydrogen bonds. In a polymer, such as cellulose, all of the side groups can interact with water, and so in each molecular conformation distinct possibilities for interactions with local water molecules will be available. Without considering loss of degrees of freedom, there is negligible energy difference between a directly intramolecular hydrogen-bonded conformation and a water-bridged conformation (Williams and Westwell, 1988Go). Therefore, rather than using intramolecular hydrogen bonds as the causal explanation of structuring, it is proposed that geometries are preferred for the ensemble as a whole, that is for molecule and water. In this interpretation cellulose has a single conformation consistent with favorable polymer–water interaction (Figure 5a). This conformation implies a rigid and the fully extended molecule. Similarly, xylan has a single favorable region that involves water bridges at the linkage (Figure 5b). On the other hand, the ß(1->4) linkage in hyaluronan is predicted to possess two competing favorable water structures (Figure 8) which have differing linkage conformations. The question of structuring in these polysaccharides then reduces to understanding how these polymers interact with water, using statistical mechanics, rather than naively assuming they are stabilized by intramolecular hydrogen bonds. Here these arguments are made for cellulose and xylan. In cellulose the argument revolves around the hydroxymethyl group, which is common to pyranoses.

First attempt at a rational reductive explanation for the extended nature of cellulose
Restricting the motion of the hydroxymethyl comes with a relatively high penalty, compared to other parts of the molecular assembly. This is because the hydroxymethyl can potentially occupy a large number of conformations, as compared to, say, a hydroxyl. Similarly, water molecules in the region of O3 and O6 have many degrees of freedom. Thus the preferred dynamic state will be that which preserves the maximum degrees of freedom in the hydroxymethyl group together with the maximum freedom of movement of local water molecules in this region. In the two-fold cellulose conformation, it is the OH3 rotamer that has lost degrees of freedom (Figure 10a). It could occupy another rotameric state if it was not involved in the hydrogen bond to O5. However, in this dynamic scenario the hydroxymethyl occupies all rotameric states, except the tg conformation (Figure 10b). Now the hydrogen bonds elucidated in Figure 3 can be seen to be part of the water structure around the hydroxymethyl group. The gt and gg states are stabilized by water bridges from O6 to O3 (in two separate orientations Figure 10c and e). More importantly, water molecules can exchange rapidly with these structures, which preserves the number of degrees of freedom available to water molecules while maintaining intramolecular hydrogen-bond networks.



View larger version (16K):
[in this window]
[in a new window]
 
Fig. 10. (a) Visualizing the conformational attractors at the linkages of cellulose. (b) Preferred orientations for hydroxymethyl groups within cellulose. (c) The most frequently observed cellulose linkage configuration with a planar structure, with an intramolecular hydrogen bond across the linkage and water bridge between O3 and O6. (d) Planar geometry, but with the hydroxymethyl closing the linkage region totally to water molecules. (e) Similar to (c) but with hydroxymethyl group on the opposite side of linkage and still involved in a water bridge.

 
In large simulations, even unfavorable molecular configurations are observed, such as that shown in Figure 11. Static visualization reveals that such a molecular configuration is perfect for coordinating water molecules within the ß(1->4) linkage. In this case the hydroxymethyl group and OH3 become heavily implicated in water coordination. Consequently, water molecules penetrate relatively deeply into the structure and cannot easily exchange with the bulk. This results in large reductions in the total numbers of degrees of freedom for both water molecules and biomolecule. Hence these molecular conformations are strongly disfavored and thus cannot be readily observed by experiments. Therefore, although the twofold conformation permits remarkably little flexibility in the chain, it maximizes the total degrees of freedom of the water and rotameric substituents (by shielding potential sites of water localization), a statistically emergent or entropic contribution to conformational stabilization. Thus it is the twofold shape that provides the minimum disturbance to the preferred statistical state of water, and the emergence of polymer order is in effect paid for by maximization of water disorder. Surprisingly, it is suggested that the extended cellulose shape arises from avoidance of strong hydrophilic, water-trapping molecular conformations. The same argument follows for both mannan and chitin, which share a similar environment with cellulose around O5.



View larger version (25K):
[in this window]
[in a new window]
 
Fig. 11. Stereo image of a linkage geometry rarely observed in the cellulose simulation, coincident with large conformational shifts in the cellulose chain. The large, solvent-accessible surface, deep into the linkage region, provides an environment for trapping water molecules and hence is disfavored.

 
On the other hand, the xylan conformation emerges because the rotamer OH3 is maximally disordered and water molecules can move more freely around the glycosidic region and exchange with bulk water. The absence of a hydroxymethyl group in the xylose sugars ensures there are no water entrapment mechanisms available at the linkages. In xylan the most disorganized state is that in which water bridges surround the linkage and thereby maintain in exchange with bulk water. The result of these water bridges is to change the average conformation of the linkage. This has the effect of breaking the twofold symmetry predicted for cellulose (see Figure 5c). Such a dynamic scenario is an impossible balancing act for the cellulose decasaccharide, and the extended planar structure emerges. Consequently the molecular length of a xylan decasaccharide is on average shorter, and the molecule is more dynamic as detected by the fluctuations in the molecular length.

Physical and biological consequences
Where does the ß(1->4) linkage of hyaluronan fit in all of this? This linkage is identical in geometry to that for chitin except for substitution of a single carboxylate group for hydroxmethyl at position C5. It could be anticipated that the incorporation of a bulkier group would restrict the dynamic space around the linkage. Paradoxically, the opposite is true; the dynamic space around the linkage is extended and multiple conformations coexist. Why is this so? The preferred explanation flows from the previous argument. The presence of the two oxygen atoms on the carboxyl group together with the actetamido group now provides a strong water coordination site on both sides of the linkage, and, in inhibiting one, the molecule opens the other. This puts a strong intrinsic dynamic instability into this linkage, as though it were see-sawing between two strong conformational attractors. One attractor is the O3 and O6 environment already described, and the other involves the carboxylate and acetamido. Again this shows that there is nothing intrinsic about the stabilized conformation in cellulose at the ß(1->4) linkage. In the simulation of hyaluronan it is present, but so are other favored geometries. The result of this degeneracy in conformations at the ß(1->4) linkage of hyaluronan is to produce, on average, a highly extended molecule, which is at the same time intrinsically unstable, thereby producing strong fluctuations in its molecular length (Figure 4d).

Considering the simulation data, it is intriguing to propose that there is a strong correlation between the predicted flexibility observed in these simulations and the solubility of these molecules. Both cellulose and chitin become insoluble beyond tetrasaccharides. It is proposed that this is resultant from the conformational restriction observed in simulations of single chains. Combined with their extended, flattened shape, this drives the molecules to prefer chain–chain associations. Xylan, although not strongly soluble, can be dispersed as a polymer in water and makes tough gels. Its predicted tendency toward a threefold shape favors hexagonal packing geometries that incorporate water. On the other hand, hyaluronan is highly soluble over a very wide molecular weight range and never forms cuttable solids unless some cross-linking factor is added, which is consistent with the prediction of a highly dynamic chain.

The consequences of gaining a microscopic understanding of these molecules, as attempted here, is undoubtedly important. Cellulose and chitin are among the most ubiquitous macromolecules on the planet, and much biological and industrial activity is centered on their production, modification, and breakdown. Similarly, hyaluronan is a major constituent of the mammalian extracellular matrix and has attracted attention in recent years as a nonimmunogenic pharmaceutical. As such, these results provide crucial new insights into the relationship between polysaccharide structure and function and clarify why such molecules have been selected as major structural molecules during evolution in an environment of liquid water. Furthermore, the importance of the ß(1->4) linkage is not restricted to polysaccharides; it is found in a range of glycoproteins and glycolipids, molecules that have been the subject of intense study recently because they are at the center of a wide variety of biological phenomena. Furthermore, extension of these studies to other linkages is now important to gain intuition into water interactions within larger classes of carbohydrates and hence widen the hypotheses set forth here. Such studies will continue to shed light on the diverse functions of glycans within living organisms.


    Materials and methods
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 References
 
Molecular dynamics simulations
Simulations used an all-atom approach in which the atoms were represented as van der Waals spheres with a partial charge. Bonds were represented using the approach of molecular mechanics and a force field suitably modified for carbohydrates (Woods et al., 1995Go). In this representation, torsional terms are calculated from ab initio molecular orbital calculations to which force field parameters are empirically fitted. The force field can then correctly reproduce torsional potentials for {alpha}- and ß-glycosdic linkages predicted by quantum calculations, using suitable partial atomic charges. In this case, partial charges were precalculated by least squares fitting to quantum mechanical electrostatic potentials, calculated with the HF/6-31G* basis set for neutral sugars and HF/6-31G** for charged sugars. Such modifications are necessary because the default hydrocarbon-based force field does not take into account electronic interactions, which are due to the presence of ring and glycosidic oxygens in the linkage region of carbohydrates; no additional torsional bias was applied beyond that predicted by ab initio calculations. These interactions, common in carbohydrate molecules, have been termed the exo-anomeric effect to explain the conformational preferences at glycosidic linkages. However, although it is strictly correct to apply such modifications to the underlying carbohydrate force field, these electronic interactions may be weakened or rendered insignificant by the presence of water, as discussed previously (Almond et al., 1997Go). Therefore, it is noteworthy that the true origin of conformational preference in aqueous solvated carbohydrate linkages, and thus the so-called exo-anomeric effect may be primarily due to interactions with water molecules, rather than electronic interactions.

In the case of cellulose, chitin, xylan, and mannan the molecular dynamics simulations were performed using the CHARMm program (Brooks et al., 1983Go). For hyaluronan the molecular dynamics simulation was performed using the tinker program as a basis (Dudek and Ponder, 1995Go) but using the same force field, as described previously (Almond et al., 2000Go). In all cases explicit water was modelled using 2000 TIP3P water molecules (Jorgensen et al., 1983Go) equilibrated at 300 K. For cellulose, chitin, mannan, and xylan the water molecules were packed into a hexagonal prism of width 3.15 nm and length 7.0 nm. In the hyaluronan simulation a rectangular box of dimension 3.2 nmx3.2 nm x6.4 nm was used. Long-range electrostatics were treated using periodic boundary conditions and a group based cut-off switched between 0.8 and 1.2 nm. Following equilibration (for 100 ps) the simulation was continued for 5 ns at constant temperature (300 K) and volume, by weak coupling to a heat bath, to construct a canonical (NVT) ensemble. Molecular dynamics integration was carried out using the leap-frog formulation (Hockney, 1970Go) of the Verlet algorithm (Verlet, 1967Go), and hydrogen covalent bond lengths 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, because it is assumed that they are well represented by the partial atomic charges and van der Waals parameters (Brady and Schmidt, 1993Go). Coordinates were written every 0.1 ps, and the nonbonded lists were updated at every step.

Analysis of molecular dynamics simulations
Glycosidic linkage conformation was represented by dihedral angles {phi} (H1-C1-O4-C4) and {psi} (C1-O4-C4-H4) defined by the hydrogen atoms at ß(1->4) linkages. Intramolecular hydrogen-bond interactions were calculated as in our previous work (Almond et al., 1997Go, 1988b) and were defined by a 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°. This (arbitrary) definition of a hydrogen bond has been used in the analysis of other carbohydrate simulations (Brady and Schmidt, 1993Go). For every frame in each of the simulations, all of the intramolecular hydrogen-bonds were identified using these criteria. Following extraction they were classified depending on their overall persistence during the simulation. Only the most persistent were kept for later analysis. The molecular length was defined between oxygen atoms in the two extreme hydroxyls. In cellulose this was O1 at one end of the molecule and O4 at the other. The contour plot in Figure 5c was created by placing all of the extracted dihedral angles (every linkage) into bins on the two-dimensional plane with resolution of 5°. These were then converted to probabilities and transformed into an energy-like function by taking the natural logarithm (Boltzmann statistics). The resulting function was contoured at relevant intervals for both cellulose and xylan simulations.

Calculation of sterically accessible conformations of cellulose
Random configurations of a cellulose decasaccharide were generated. Each conformation was then tested for any atomic overlap. In this process the effective carbon and oxygen hard-sphere diameters were taken as 0.32 nm and 0.27 nm, respectively (Pauling et al., 1951Go). Conformations without steric clashes were accepted, and their molecular length was binned to produce the curve of Figure 9.


    Acknowledgements
 
A.A. was funded by a Wellcome Trust Prize Travelling Research Fellowship, grant reference number 058154. J.S. was also funded by the Wellcome Trust on a Showcase Award Scheme.

1 To whom correspondence should be addressed; e-mail: andrew.almond{at}bioch.ox.ac.uk Back


    References
 Top
 Abstract
 Introduction
 Results
 Discussion
 Materials and methods
 References
 
Almond, A., Sheehan, J.K., and Brass, A. (1997) Molecular dynamics simulations of the two disaccharides of hyaluronan in aqueous solution. Glycobiology, 7, 597–604.[Abstract]

Almond, A., Brass, A., and Sheehan, J.K. (1998a) Deducing polymeric structure from aqueous molecular dynamics simulations of oligosaccharides: solution simulations of hyaluronan tetrasaccharides compared with hydrodynamic and X-ray fibre diffraction data from the polymer. J. Mol. Biol., 284, 1425–1437.[CrossRef][ISI][Medline]

Almond, A., Brass, A., and Sheehan, J.K. (1998b) Dynamic exchange between stabilized conformations predicted for hyaluronan tetrasaccharides: comparison of molecular dynamics simulations with available NMR data. Glycobioogy, 8, 973–980.[Abstract/Free Full Text]

Almond, A., Brass, A., and Sheehan, J.K. (2000) Oligosaccharides as model systems for understanding water-biopolymer interaction: hydrated dynamics of a hyaluornan decamer. J. Phys. Chem. B, 104, 5634–5640.[CrossRef][ISI]

Aspinall, G.O. (1985) The polysaccharides. New York: Academic Press.

Atkins, E.D.T., Phelps, C.F., and Sheehan, J.K. (1972) The conformation of the mucopolysaccharides. Hyaluronates. Biochem. J., 128, 1255–1263.[ISI][Medline]

Atkins, E.D.T., Meader, D., and Scott, J.E. (1980) Model of hyaluronic acid incorporating four intra-molecular hydrogen-bonds. Int. J. Biol. Macromol., 2, 318–319.[CrossRef][ISI]

Atkins, E.D.T., Farnell, S., Mackie, W., and Sheldrick B. (1988) Crystal structure and packing of mannan I. Biopolymers, 27, 1097–1105.[ISI]

Brady, J.W. (1989) Molecular dynamics simulations of {alpha}-D-glucose in aqueous-solution. J. Am. Chem. Soc., 111, 5155–5165.[ISI]

Brady, J.W. (1990) Molecular dynamics simulations of carbohydrate molecules. Adv. Biophys. Chem., 1, 155–202.

Brady, J.W. and Schmidt, R.K. (1993) The role of hydrogen-bonding in carbohydrates: molecular dynamics simulations of maltose in aqueous solution. J. Phys. Chem., 97, 958–966.

Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., and Karplus, M. (1983) CHARMm: a program for macromolecular energy minimization and dynamics calculations. J. Comp. Chem., 4, 187–217.[ISI]

Duan, Y. and Kollman, P.A. (1998) Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science, 282, 740–744.[Abstract/Free Full Text]

Dudek, M.J., and Ponder, J.W. (1995) Accurate modeling of the intramolecular electrostatic energy of proteins. J. Comput. Chem., 16, 791–816.[ISI]

Duus, J.Ø., Gotfredsen, C.H., and Bock, K. (2000) Carbohydrate structural determination by NMR: modern methods and limitations. Chem. Rev., 100, 4589–4614.[CrossRef][ISI][Medline]

Franks, F. (1983) Water. London: Royal Society of Chemistry.

Gardner, K.H. and Blackwell, J. (1974) The structure of native cellulose. Biopolymers, 13, 1975–2001.[ISI]

Gardner, K.H. and Blackwell, J. (1975) Refinement of the structure of ß-chitin. Biopolymers, 14, 1581–1595.[ISI][Medline]

Grigera, J.R. (1988) Conformation of polyols in water—molecular dynamics simulation of mannitol and sorbitol. J. Chem. Soc., Faraday Trans. I, 84, 2603–2608.[ISI]

Haigler, C.H., Ivanova-Datcheva, M., Hogan, P.S., Salnikov, V.V., Hwang, S., Martin, K., and Delmer, D.P. (2001) Carbon partitioning to cellulose synthesis. Plant Mol. Biol., 47, 29–51.[CrossRef][ISI][Medline]

Hockney, R.W. (1970) The potential calculation and some applications. Meth. Comp. Phys., 9, 135–211.

Iozzo, R.V. (1998) Matrix proteoglycans: from molecular design to cellular function. Ann. Rev. Biochem., 67, 609–652.[CrossRef][ISI][Medline]

Jorgensen, W.L., Chandrasekhar, J., Madura, J.D., Impey, R.W., and Klein, M.L. (1983) Comparison of simple potential functions for simulating liquid water. J. Chem. Phys., 79, 926–935.[CrossRef][ISI]

Karnezis, T., McIntosh, M., Wardak, A.Z., Stanisich, V.A., and Stone, B.A. (2000) The biosynthesis of beta-glycans. Trends Glycosci. Glycotech., 12, 211–227.[ISI]

Kirschner, K.N. and Woods, R.J. (2001) Solvent interactions determine carbohydrate conformation. P. Natl. Acad. Sci. USA, 98, 10541–10545.[Abstract/Free Full Text]

Koehler, J.E.H., Saenger, W., and van Gunsteren, W.F. (1988) Conformational differences between {alpha}-cyclodextrin in aqueous-solution and in crystalline form—a molecular dynamics study. J. Mol. Biol., 203, 241–250.[ISI][Medline]

Lee, J.Y. and Spicer A.P. (2000) Hyaluronan: a multifunctional, megaDalton, stealth molecule. Curr. Opin. Cell. Biol., 12, 581–586.[CrossRef][ISI][Medline]

Lyon, M. and Gallagher J.T. (1998) Bio-specific sequences and domains in heparin sulphate and the regulation of cell growth and adhesion. Matrix Biol., 17, 485–493.[CrossRef][ISI][Medline]

Muzzarelli, R.A.A. and Muzzarelli, C. (1998) Native and modified chitins in the biosphere. In Nitrogen-containing macromolecules in the bio- and geosphere. ACS Symposium Series, 707, 148–162.

Nieduszynski, I.A. and Marchessault, R.H. (1972) Structure of ß(1->4)-xylan hydrate. Biopolymers, 111, 1335–1344.

Pauling, L., Corey, R.B., and Branson H.R. (1951) Structure of proteins: two hydrogen-bonded helical configurations of the polypeptide chain. Proc. Natl Acad. Sci., 37, 205–211.[ISI][Medline]

Rao, V.S.R., Qasba, P.K., Balaji, P.V., and Chandrasekhan, R. (1998) Conformation of carbohydrates. Amsterdam: Harwood Academic Publishers.

Sheehan, J.K. and Atkins, E.D.T. (1983) X-ray fibre diffraction study of the conformational changes in hyaluronate induced in the presence of sodium, potassium and calcium cations. Int J. Biol. Macromol., 5, 215–221.[CrossRef][ISI]

Sugiyama, J. and Imai, T. (1999) Aspects of native cellulose microfibrils at molecular resolution. Trends Glycosci. Glycotech., 11, 23–31.[ISI]

Tonnessen, B.A. and Ellefsen, Ø. (1971) Investigations of the structure of cellulose and its derivatives. F. Submicroscopical investigations. In Bikales, N.M. and Segal, L. (eds.), Cellulose and cellulose derivatives, Part 4. New York: Wiley Interscience, pp. 265–304.

van Gunsteren, W.F. and Berendsen, H.J.C. (1977) Algorithms for macromolecular dynamics and constraint dynamics. Mol. Phys., 34, 1311–1327.[ISI]

Verlet, L. (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 159, 98–103.[CrossRef][ISI]

Williams, D.H. and Westwell, M.S. (1998) Aspects of weak interactions. Chem. Soc. Rev., 27, 57–63.[ISI]

Winter, W.T., Smith, P.J.C., and Arnott, S. (1975) Hyaluronic acid: structure of a fully extended 3-fold helical sodium salt and comparison with the less extended 4-fold helical forms. J. Mol. Biol., 99, 219–235.[ISI][Medline]

Woods, R.J., Dwek, R.A., Edge, C.J., and Fraser-Reid, B. (1995) Molecular mechanical and molecular dynamical simulations of glycoproteins and oligosaccharides. 1. GLYCAM-93 parameter development. J. Phys. Chem., 99, 3832–3846.[ISI]