Potential of Mean Force Conformational Energy Maps for Disaccharide Linkages of the Burkholderia multivorans Exopolysaccharide C1576 in Aqueous Solution

Abstract

Potential of Mean Force Ramachandran energy maps in aqueous solution have been prepared for all of the glycosidic linkages found in the C1576 exopolysaccharide from the biofilms of the bacterial species Burkholderia multivorans, a member of the Burkholderia cepacian complex that was isolated from a cystic fibrosis patient. C1576 is a rhamnomannan with a tetrasaccharide repeat unit. In general, for the four linkage types in this polymer, hydration did not produce dramatic changes in the Ramachandran energy surfaces, with the 3-methyl-α-d-rhamnopyranose-(1→3)-α-d-rhamnopyranose case exhibiting the greatest hydration change, with the global minimum energy conformation shifting by more than 80° in ψ. However, hydration did reduce the rigidity of all the linkages, increasing the overall flexibility of this polysaccharide.

Graphical Abstract

Introduction

Ramachandran-type conformational energy maps are important in polymer theory as they determine the types of overall conformations that are possible for polymers.^{1, 2} Importantly, they rule out many conformations that would produce steric clashes between successive residues in a polymer, and using well-parameterized molecular mechanics force fields, they can identify preferred low energy conformers, their relative energies, and the low energy pathways and energy barriers for transitions between conformations.^{3, 4} These maps do not capture long-range interactions between residues more distantly separated in sequence, such as occur in folded proteins or helices with low pitches. Such interactions are usually “long-range” in sequence separation only, and often involve direct short-range interactions such as steric clashes or hydrogen bonds, like those that occur between residues i and (i+4) in the alpha helical conformations of polypeptide chains. In addition, it is possible that other environmental effects, most importantly arising from solvation, can alter the relative energetics of conformers on the conformational energy surface. This can be particularly true in some cases of aqueous solvation when there is a stabilizing hydrogen bond between successive residues in a polymer, since water can potentially exchange for the donor and acceptor groups, producing two polymer-water hydrogen bonds. Previous work has shown that in the case of conformational energy maps for disaccharides, such hydrogen bond exchange involving water can produce dramatic changes in the conformational energy landscape and lead to very different polymer conformations in aqueous solution from those that might exist in an anhydrous fiber.^{5, 6}

Recently we reported Ramachandran conformational energy maps⁷ for all of the previously uncharacterized linkages of the C1576 exopolysaccharide found in the biofilms formed by the bacterial species Burkholderia multivorans,^{8, 9} a member of the Burkholderia cepacian complex that was isolated from a cystic fibrosis patient. This polysaccharide is a rhamnomannan with a tetrasaccharide repeat unit,⁹ with the sequence −[3-α-d-Man-(1→2)-α-d-Man-(1→2)- α -d-Rha-(1→3)-α-d-Rha-(1→]_n−, where approximately 50% of the O3 hydroxyl groups of the first rhamnose residues are randomly methylated (the second rhamnose residues of the repeat unit are not methylated), resulting in several possible variants of the disaccharide linkages involving the rhamnose residues, with six possible linkages in all. Figure 1 displays molecular representations of each of the disaccharide linkages found in this repeat sequence.

Figure 1.

Molecular structure of each disaccharide at its respective minimum energy dihedral angles from PMF calculations (see text and Fig. 3).

For disaccharides, it is convenient to take the glycosidic linkage torsion angles ϕ and ψ connecting the two sugar rings, defined as O5-C1-O3’-C3’ and C1-O3’-C3’-C2’ for the (1→3) linkages in the C1576 polysaccharide and O5-C1-O2’-C2’ and C1-O2’-C2’-C1’ for the (1→2) linkages, as the appropriate degrees of freedom specifying disaccharide conformation. This choice reduces the problem of conformational description to two dimensions. However, unlike polypeptides, the sugar rings also have conformational freedom, with multiple possible ring forms and hydroxyl group conformations. For most sugar monomers, the energies of these ring conformers are such that one chair form (usually ⁴C₁) is much lower than all of the others, so that only that one ring conformer needs to be used in the conformational energy mapping,⁸ but all orientations of the hydroxyl groups need to be checked, not only because of the associated dipole orientation, but more importantly, because of the potential for hydrogen bonding involving these groups. With these assumptions, the entire conformational energy surface for linkages can be mapped out.

For neutral (non-polyelectrolyte) polymers, these vacuum Ramachandran energy maps are generally sufficient for describing polymer chain conformations, and typically the trajectories traced out by vacuum molecular dynamics (MD) simulations of these molecules will follow the contours of the maps quite closely, which can be taken as corroboration of the correctness of the maps. However, the presence of water can significantly affect the dynamics and conformational preferences of the disaccharides, particularly in situations where intramolecular hydrogen bonding is possible. In such cases, potential of mean force (PMF) free energy maps need to be calculated which incorporate both entropic effects like disaccharide configurational freedom and solvent structuring, as well as direct enthalpic contributions from solvent hydrogen bonds. Previously a preliminary estimate of such free energy effects was made from calculated trajectory probability densities in the case of the C1576 polysaccharide for two of its linkages: 3-methyl-α-d-rhamnopyranose-(1→3)-α-d-rhamnopyranose and α-d-mannopyranose-(1→2)-3-methyl-α-d-rhamnopyranose.⁷ The present report describes the systematic calculation of the PMF free energy maps for all of the linkages of C1576 in aqueous solution using weighted histogram umbrella sampling methods.^10–12

Methods

The aim of a PMF calculation approach is to describe the free energy landscape within a subspace of predefined reaction coordinates with the greatest accuracy and a minimal sampling effort. Through a combination of optimally selected reaction coordinates, sampling size, and method, such PMF maps of the relevant coordinate space can be constructed. In the present study, PMF calculations were carried out employing an umbrella sampling method over the entire region of ϕ and ψ and the data was then combined using a weighted histogram analysis method (WHAM).^10–12

Umbrella sampling^13–22 consists of running separate “windows” of the reaction coordinate ranges simultaneously. This parallelization can greatly increase the efficiency of the overall simulation, limited mostly by the number of computational processors available. First, the reaction coordinate space is divided into overlapping segments, or “windows”. Each of these coordinate-range windows consists of an independent simulation or simulations where the system is permitted to sample only within that coordinate range. This is typically achieved by applying a harmonic constraint to the selected reaction coordinate: U_i(φ) = k_i(φ − φ_0,i)², with the equilibrium position, φ_0,i, of the harmonic constraint defining the center of window i, and the force constant, k_i, defining the corresponding width. The center and width of each window, determined by the selection of k_i and φ_0,i, should ensure that the calculated probability distributions of ϕ and ψ can overlap with those of simulations of neighboring windows with sufficient trajectory probability density to allow for normalization. By allowing neighboring windows to overlap and making sure there are enough windows to cover the entire reaction coordinate space, a PMF can be calculated by properly combining the data from each simulation through the use of WHAM, giving normalized statistical weighting to the overlapping regions between windows.

In the present study, two dimensional windows of 5° × 5° were chosen to cover the entire (ϕ, ψ) region, resulting in a total grid of 73 × 73 windows in the reaction coordinate space. Each of the disaccharides was modeled surrounded by water molecules in a cubic box 24.6 Å in length with periodic boundary conditions. The simulation box was prepared by placing the disaccharide in the center of a previously equilibrated TIP3P^{23, 24} water box containing 512 water molecules and removing those solvent molecules that overlapped with the disaccharide. The simulation system in each window was first prepared using the CHARMM molecular mechanics program^{25, 26} and the CHARMM36²⁷ force field parameters for carbohydrates,^{28, 29} using procedures described previously⁷ at a constant pressure of 1 atm and a constant temperature of 300 K. During the preparation stage the system is heated and equilibrated for 50 ps. The prepared system was then converted³⁰ into the format of the AMBER molecular dynamics program³¹ for better computational efficiency when using the XSEDE supercomputer COMET³² to carry out the 73×73 simulations for each disaccharide. Using AMBER, the system was first heated to 300 K and then equilibrated for 100 ps at 1 atm, after which 1 ns of umbrella sampling simulation time was carried out for each torsion angle window. The force constant for the harmonic umbrella constraint potential was 300 kcal/mol/radians² in each case. For those grid points that corresponded to very high energies on the vacuum energy surface, if the initial constrained simulation in solution did not produce a significant lowering in the system energy without distortions of the ring geometries or stereochemistries, which were continuously monitored, then the simulation was terminated and the grid point assigned the energy of the vacuum surface. The set of energies on the 73×73 conformational space grid were then used to construct a contour map using the spline function in MATLAB.³³ Statistical sampling overlap between adjacent windows was excellent in all cases; Figure S1 in the Supplementary Material displays typical examples.

In addition, in order to test the accuracy of the computed PMFs, a 10 ns conventional (unconstrained) molecular dynamics (MD) simulation was performed for each disaccharide in aqueous solution with the initial structure being that of the global minimum on the PMF. The simulation procedures and conditions were as previously described, with the difference in that a strong constraining force was turned on during the heating and equilibration, with a force constant of 300 kcal/mol/radians², which was then turned off during the production simulation. These were independent simulations that were not used in the calculations of the PMF. A further set of test trajectories starting from a very high energy conformer on the maps was conducted to determine if unmapped very high-energy barriers or ring conformational changes prevented such unrealistic starting conditions for the trajectories from finding their global minima.

In order to avoid computational artifacts the angles ϕ and ψ were defined as O5-C1-O3’-C3’ and C1-O3’-C3’-C2’ for (1→3) connections or O5-C1-O2’-C2’ and C1-O2’-C2’-C1’ for (1→2) connections, using heavy atoms rather than the proton-based definitions used in NMR work. The conversion to the proton-based definition can be made easily by subtracting 120° from each.

Results and Discussion

The vacuum Ramachandran energy contour maps for these disaccharides were calculated previously⁷ and are shown for reference in Figure 2. Overall, these vacuum Ramachandran maps give a good first estimate of the conformation of the polysaccharide. The corresponding PMF conformational free energy maps in aqueous solution for each of these six C1576 disaccharides are shown in Figure 3, where the global minimum on each is indicated with a red “X”. The approximate global minimum energy conformation was obtained from the spline mapping of the calculated grid energy values, and its exact position in each case was verified through an additional unconstrained MD simulation of 10 ns of the disaccharide using the pre-determined approximate minimum energy structure in aqueous solution as the starting conformation. The color contours shown on the map are at uniform 1 kcal/mol intervals above this global minimum energy conformation. The large white spaces on the maps are high energy regions due to steric clashes of atom positions at those dihedral angle orientations. The six maps in Figure 3 each have only one very low energy region at ϕ values ranging from approximately 50° to 100° and ψ values ranging from −20° to −150°. This indicates that the polysaccharide formed by these disaccharides will be generally more flexible in the ψ coordinate and less so in the ϕ coordinate in aqueous solution. Of the six disaccharides, the most flexible are α-d-mannopyranose-(1→2)-α-d-mannopyranose and α-d-mannopyranose-(1→2)-α-d-rhamnopyranose (Figures 3a and 3b), with a range of about 50° degrees in the ϕ coordinate and 130° in the ψ coordinate. The next most flexible would be the α-d-mannopyranose-(1→2)-3-methyl-α-d-rhamnopyranose disaccharide (Figure 3c), with a range of about 50° in the ϕ coordinate and 80° in the ψ coordinate. The least flexible disaccharides have rhamnose at the non-reducing end: α-d-rhamnopyranose-(1→3)-α-d-rhamnopyranose, 3-methyl-α-d-rhamnopyranose-(1→3)-α-d-rhamnopyranose, and α-d-rhamnopyranose-(1→3)-α-d-mannopyranose (Figures 3d, e, and f) with a range of about 50° in both the ϕ and ψ coordinates.

Figure 2.

Vacuum Ramachandran maps for each of the 6 disaccharides. On each map the global minimum is indicated by a red “X”. Contour levels are indicated in kcal/mol above the global minima.⁷

Figure 3.

Ramachandran conformational free energy maps (PMFs) for the disaccharide linkages of C1576 in aqueous solution. The global minima are indicated with a red “X”. Energy contours are shown from 1 to 10 kcal/mol above the global minimum. Each plot is labeled with a shorthand notation where “m” refers to methylated rhamnose.

The trajectories of the 10 ns unconstrained MD simulations of each solvated disaccharide starting from their respective identified minima are shown in Figure 4, superimposed over the PMF surfaces from Figure 3. These simulations are independent and not included in the PMF calculations. As can be seen, the trajectories are all well confined within the low energy region of each respective PMF map, with occasional short excursions into the slightly higher energy regions as expected due to the energy changes from thermal fluctuations. The probability distributions of the dihedral angles from the unconstrained trajectories shown in Figure 4 conformed closely to the calculated PMF contours (Figure S2), further demonstrating their validity as good descriptions of the free energy each molecule experiences in aqueous solution.

Figure 4.

Dihedral angle trajectories of 10 ns unconstrained solvated MD simulations, each starting from the calculated global free energy minimum conformation of the Ramachandran maps shown in Figure 3.

By comparison with Figure 2 it can be seen that in vacuum most of the disaccharides have multiple small low energy regions which are not seen in the solution PMF. These small “ripples” on the vacuum surface result partially from longer-range electrostatic sums that vary with conformation but which are smoothed out in solution by solvent dielectric screening, hydrogen bonding and solvent-solvent interactions. The solution PMFs are characterized instead by a single larger low energy region. This larger low energy valley is solution-induced as the water molecules form hydrogen bonds with the molecule, allowing it more flexibility due to entropy. The global minimum of each disaccharide also shifted when comparing the vacuum and solution energy maps, although in three of the cases the shift is small. A summary of the minimum energy positions for both vacuum and solution energy maps is shown in Table 1. One of the disaccharides involving a methylated rhamnose, the 3-methyl-α-d-rhamnopyranose-(1→3)-α-d-rhamnopyranose case, exhibits the largest conformational shift between the vacuum and solution energy maps. Interestingly, all of the maps feature a new lower energy region in solution in the vicinity of (−85°, −170°) that is absent from the vacuum maps, although still much higher in energy than the global energy valley.

Table 1.

Summary of the locations of the global minimum in vacuum and in solution and the shift between them.

Disaccharide	Minimum in vacuum	Minimum in solution	Minimum shift
Man(1→2)Man	(79.7°, −51.3°)	(81.5°, −81.5°)	(−1.8°, 30.2°)
Man(1→2)Rha	(81.0°, −61.1°)	(81.5°, −83.5°)	(−0.5°, 22.4°)
Man(1→2)m-Rha	(76.1°, −132.0°)	(72.5°, −132.5°)	(−3.6°, −0.5°)
Rha(1→3)Rha	(76.4°, −134.2°)	(68.5°, −134.5°)	(7.9°, 0.3°)
m-Rha(1→3)Rha	(89.3°, −49.1°)	(71.5°, −132.6°)	(17.8°, 83.5°)
Rha(1→3)Man	(75.8°, −135.3°)	(69.5°, −133.5°)	(6.3°, −1.8°)

As a further validation of the solution PMF maps, for each disaccharide a 10 ns conventional MD solution simulation was calculated starting from the very high energy (−50°, 50°) position to determine if the molecule could easily find its lowest energy conformation starting from such an unrealistic geometry. The resulting trajectory in each case is superimposed over the respective PMF in Figure 5. As can be seen, in all cases, the molecule spent only a very short time in the high energy region before quickly finding its way to the global low energy valley and subsequently spent the rest of its time within the low energy region. Of particular interest is the case shown in Figure 5e for the methylated-Rha-(1→3)-Rha. In this case, this dimer has the widest lower energy “valley” on the PMF at ψ around 50°, and the simulated disaccharide was able to access the global minimum conformation through that route rather than going directly to ψ around −50° or lower. Because of the rapid relaxation time for liquid water, these results are not sensitive to trajectory length; extending the methylated-Rha-(1→3)-Rha simulation by an order of magnitude to 100 ns produced no changes in the conformational sampling (see Figure S3 in the Supplementary Material), nor did raising the temperature to 310° K (Figure S4).

Figure 5.

10 ns simulations for each linkage type in aqueous solution, starting in each case from the conformation at (−50°, 50°)

Conclusions

In some previously-studied disaccharides, aqueous solvation produced dramatic changes in the Ramachandran conformational energy maps. For example, in the α-(1→4)-linked disaccharide of D-xylose (“dixylose”)⁵ and for neocarrabiose,³⁴ the global minimum energy conformations in vacuum are stabilized by hydrogen bonds between the two linked sugar rings. In both cases, upon solvation, a water molecule bridges between the hydroxyl groups previously directly hydrogen bonded to each other in vacuum, producing a significant conformational shift and the appearance of a new global minimum free energy conformation in solution that was not even a stable minimum on the vacuum map, with the disappearance or significant destabilization of the vacuum minimum energy conformation. No such hydrogen bond exchange was observed in the disaccharide linkages studied here except for the α-d-mannopyranose-(1→2)-α-d-mannopyranose case. For this disaccharide linkage in vacuum, there is a hydrogen bond between the two primary alcohol groups (see Figure 2 of Jou et al.⁷) which is replaced in solution by a bridging water molecule between these two hydroxyl groups (Figure 7 of Jou et al.),⁷ which shifts the global minimum energy conformation ψ angle by ~30°. For the 3-methyl-α-d-rhamnopyranose-(1→3)-α-d-rhamnopyranose case the vacuum global minimum energy conformation at (89.3°, −49.1°), which is not hydrogen bonded between rings,⁷ shifted more than 80° in ψ to (71.5°, −132.6°) on the solvated free energy surface, the largest solvent effect observed in this set, but no bridging water molecule inserted between the two rings. Apparently the shift in minimum energy conformation is simply because the overall hydration pattern is just lower in energy on average for that arrangement, perhaps because hydration allows larger fluctuations and thus higher entropy. In the other linkages, hydration produced more modest shifts in the global minimum energy conformation, and in general tended to allow somewhat greater fluctuations, but the principal low-energy valley on each map remained the main low energy region in solution.

The most consistent effect of solvation on these six linkages is to allow greater flexibility in ϕ when ψ in the approximate range −30° to −130°. In all six maps a new higher-energy minimum appears around (−85°, −100°). This minimum is most significant and the most stable in α-d-mannopyranose-(1→2)-α-d-mannopyranose, although shifted to even more negative ψ values, with a new minimum around (−90°, −160°), and with a clear pathway over a col around a ϕ value of −120°, leading down to the global minimum energy valley (Figure 6). However, these new minima do not appear to be stabilized by water molecules bridging between the rings. Apparently the overall organization of the hydration shell for those conformations is sufficiently favorable to stabilize otherwise high energy arrangements on the vacuum surface. Nonetheless, these new minima are so much higher in energy, 8–10 kcal/mol above the global minimum, that they are not even briefly stable, and only serve to facilitate rotational transitions in ϕ (Figure 6b).

Figure 6.

Left, the α-d-mannopyranose-(1→2)-α-d-mannopyranose structure corresponding to the minimum around (−85°,−160°) on the solution PMF, illustrating the close approach of the H5-O3’ atomic pair in that conformation; Right, the trajectory followed by an unconstrained solution simulation begun in this conformation as it rapidly transitioned to the global minimum conformation around (81.5°, −81.5°) by passing over the energy col on that surface and rotating through >190° in ϕ.

The existence of this new low energy region on all of these (1→2) and (1→3) linkage surfaces, along with a widening of the global minimum wells into negative ϕ values suggests that for the C1576 polysaccharides in aqueous solution, there is considerable new flexibility in the ϕ coordinate in this negative ψ range to match the greater freedom in ψ in the positive ϕ range [0°,180°]. The shifts in lowest energy linkage conformations means that there will be changes in the overall “ideal” polymer conformation, but since the changes are not dramatic, the change in polymer conformation is also modest, as can be seen in Figure 7. Thus, this polysaccharide appears to be an example of a biopolymer system where hydration is relatively unimportant structurally.

Figure 7.

Example short-chain polymer segments (7 repeat units) constructed using the global minimum energy conformations for each linkage. In each case the fourth repeat unit is colored yellow for reference. (a) superposition of these chains, aligned on the fourth repeat unit (again in yellow), with the unmethylated solvated chain in red, the randomly methylated solvated chain in blue, and the unmethylated vacuum chain shown in cyan for comparison; (b) an unmethylated solvated ideal chain; (c) a randomly methylated chain (in this case, with substitutions at 3,5,6 and 7).

Highlights.

• The novel C1576 exopolysaccharide from Burkholderia multivorans biofilms in cystic fibrosis patients has a high rhamnose content and previously uncharacterized glycosidic linkages

• Potential of mean force Ramachandran conformational energy maps for each linkage in aqueous solution were prepared using molecular dynamics simulations and free energy methods to determine how solvation affects the C1576 polysaccharide conformation

• Unlike many other polysaccharides, hydration of these linkages was found to produce no significant changes in conformation for this polysaccharide

• However, hydration did increase the polysaccharide flexibility, which could contribute to biofilm matrix formation