On the Conformational Properties of Amylose and Cellulose Oligomers in Solution

Molecular dynamics (MD) simulations were used to monitor the stability and conformation of double-stranded and singlestranded amyloses and single-stranded cellulose oligomers containing 9 sugar moieties in solution as a function of solvent composition, ionic strength, temperature, and methylation state. This study along with other previous studies suggests that hydrogen bonds are crucial for guaranteeing the stability of the amylose double helix. Single-stranded amylose forms a helical structure as well, and cellulose stays highly elongated throughout the simulation time, a behavior that was also observed experimentally. In terms of coordination of solute hydroxyl groups with ions, amylose shows entropy-driven coordination of calcium and sulfate ions, whereas cellulose-ion coordination seems to be enthalpy-dominated. This indicates that entropy considerations cannot be neglected when explaining the structural differences between amyloses and celluloses.


Introduction
Amylose and cellulose are linear polymers of glucose linked with 1,4-bonds.The main difference is the anomeric configureration: amylose's glucose units are linked with α(1 → 4) glycosidic bonds, whereas cellulose's monomeric units are linked by β(1 → 4) glycosidic bonds.This different kind of bonding causes amylose to form helical structures and cellulose to form straight polymer chains.
Amylose occurs in different forms, the A, B, V, and other forms [1].The A and B forms both feature left-handed helices with six glucose units per turn and seem to differ only in the packing of the starch helices.The V form of amylose is obtained through cocrystallization with compounds such as iodine, DMSO, alcohols, or fatty acids [2,3].The helical conformations of B-and V-amylose show differences [4][5][6].
Cellulose is a linear polymer and is the most abundant natural polymer on earth.Cellulose's structure and properties have been investigated extensively, but still there are uncertainties about cellulose's crystal structure [7][8][9].X-ray scattering and electron diffraction experiments show that cellulose forms aggregates to sheet-like structures with the cellulose molecules in elongated conformation.These structural differences are the reason why amyloses and celluloses have very different physical and biological properties [10].Amylose is poorly soluble in water and forms suspensions, in which its helicity is preserved.Cellulose fibers are insoluble in water.
Computer simulations of these systems can be done to get atomic-level insight into the behavior of these molecules and to perform computational studies of their properties.A Monte-Carlo computer simulation of double-helical amylose in water by Eisenhaber and Schuler [11] suggests that a lefthanded antiparallel double helix fits best to the structure of liquid water.Regular water bridges forming a network around the duplex were observed.
Previous molecular dynamics (MD) studies on amylose and cellulose have been done by Yu et al. [12].Fragments of these molecules were methylated at different positions, and their stabilities were monitored.The authors concluded that single helices are more destabilized by methylation of amylose's O-2 and O-3 moieties than by methylation at O-6 , but that the methylation of O-6 destabilizes double helices more.
In the present work simulations of double-stranded and single-stranded amyloses and single-stranded cellulose oligomers consisting of 9 sugar moieties are analyzed, and the stability of particular structures of these molecules is studied as a function of type of solvent, ionic strength, temperature, and methylation state.

Molecular Dynamics Simulations.
MD simulations were performed with the GROMOS software package [13][14][15] using the force-field parameter set 53A6 [16], which treats aliphatic carbons as united atoms.Sugar parameters have been optimized for the GROMOS force field by Lins and Hünenberger [17].The MD simulations performed for molecules consisting of 9 sugar units are summarized in Table 1.Amylose's and cellulose's initial coordinates were generated with the INSIGHTII software package (Accelerys Inc., San Diego, Calif, USA).Amylose was modeled into a double helix.Initial solute conformations of the amylose double-helix were the regular helices built from the data by Imberty et al. [18].This model is characterized by torsional angles of φ = ∠(O5, C1, O4 , C4 ) = 84 • and ψ = ∠(C1, O4 , C4 , C5 ) = −145 • .To further investigate the role of hydrogen bonds in helix stability, simulations with all nonbonded interactions between solute atoms involved in hydrogen bonds turned off were carried out (label: noHB) as well as simulations with hydroxy-groups involved in hydrogen bonds methylated (label: met).In the topologies for the simulations with excluded hydrogen bonds, Lennard-Jones interactions between hydrogen-bonded atoms have been set to zero.For the simulations of single-stranded amylose one strand was removed from the double-helical starting structure.The simulations involving cellulose oligomers started from an extended conformation with the angles φ = −120 • and ψ = −120 • .The simple-point-charge (SPC) water model [19] was used to describe the solvent molecules.In some simulations DMSO [20] was used as a solvent (label: DMSO).In the simulations the solvent molecules were added around the solute within a rectangular box for (double-stranded) amylose and cellulose with a minimum distance of 1.4 nm between the solute atoms and the walls of the periodic box.In the simulations rototranslational constraints have been used [21].In some of the simulations in aqueous solution, ions (SO 2− 4 and Ca 2+ ) were included (Table 1).The initial placement of the ions was random.All the bonds and the bond angles of the solvent molecules were constrained with a geometric tolerance of 10 −4 using the SHAKE algorithm [22].The steepest-descent energy minimization without any restraints of all systems was performed to relax the solute-solvent contacts.The energy minimizations were terminated when the energy change per step became smaller than 0.1 kJ mol −1 .For the nonbonded interactions, a triple-range method with cutoff radii of 0.8/1.4nm was used.Short-range van der Waals and electrostatic interactions were evaluated every (time) step based on a charge-group pairlist.Medium-range van der Waals and electrostatic interactions, between pairs at a distance longer than 0.8 nm and shorter than 1.4 nm, were evaluated every fifth (time) step, at which (time) point the pair list was updated.Outside the longer cutoff radius a reaction-field approximation [23] was used with a relative dielectric permittivity of 66 [24].The initial velocities of the atoms were assigned from a Maxwell distribution at 50 K.For amylose four 50 ps periods of MD simulation with harmonic position restraining of the solute atoms with force constants of 1.0 and 5.0 kJ mol −1 nm −2 were performed to equilibrate further the systems at 50 K, 100 K, 200 K, and 278/313 K, respectively.For cellulose five 50 ps periods of MD simulation with harmonic position restraining of the solute atoms with force constants of 2.5 • 10 4 kJ mol −1 nm −2 , 1.0 • 10 4 kJ mol −1 nm −2 , 1.0 • 10 3 kJ mol −1 nm −2 , 1.0 • 10 2 kJ mol −1 nm −2 , and 5.0 kJ mol −1 nm −2 were performed to equilibrate further the systems at 50 K, 100 K, 200 K, 278/313 K, and 278/313 K, respectively.During the equilibration, solvent and solute degrees of freedom were independently, weakly coupled to a temperature bath at the given temperature with a relaxation time of 0.1 ps [25].In the further simulations, the center of mass motion of the whole system was set to zero every 1000 time steps.The systems were also weakly coupled to a pressure bath of 1 atom with a relaxation time of 0.5 ps and an isothermal compressibility of  0.4575 × 10 −3 (kJ mol −1 nm −3 ) −1 .The trajectory coordinates and energies were saved every 0.5 ps for analysis.

Analysis.
Analyses were done with the analysis software packages GROMOS++ [15] and esra [26].Radii of gyration were calculated to observe the level of compactness of the simulated molecules.Structural information on ionic solutions was obtained from the radial distribution functions g(r).For amylose, percentages of inter-and intramolecular hydrogen bonds were calculated using a maximum distance criterion of 0.25 nm between the hydrogen atom and the acceptor atom and a minimum angle criterion of 135 • for the donor-hydrogen-acceptor angle.

Double-Stranded
Amylose in Pure Solvent.The radii of gyration of amylose in different solvents and methylation states are shown in Figure 1.Exclusion of interactions between atoms that form hydrogen bonds do not influence the behavior of the radii of gyration significantly.Hydrogen bond percentages are shown in Table 2. Excluding the hydrogen bond interaction in the simulation makes hydrogen bonds as analyzed vanish.Simulating in DMSO increases the solute-solute hydrogen bonding, and higher percentages can be observed.Methylation of the structure reduces solutesolute hydrogen bonding to zero.Still the structures of the methylated and unmethylated cases yield similar radii of gyration (Figure 1).Their structures are different, however, comparing the final structures (Figure 2).Amylose with

Double-Stranded
Amylose in Ionic Solution.Amylose adopts lower radii of gyration at 313 K than at 278 K (Figure 1).Hydrogen bond analysis (Table 3) shows lower hydrogen bond percentages at higher temperature, but on the other hand more favorable sulfate coordination to solute hydroxyl groups than at lower temperature.In Figure 3 the radial distribution functions for the different atom pairs are shown.The affinity of sulfate to calcium is higher at higher temperature, at least for the first solvation shell (Figure 3(a)).This suggests that the coordination of calcium and sulfate is entropy-driven.Both calcium and sulfate coordinate to the solute's hydroxyl groups that are not on the inner side of the helix (O 2 and O 3 ), but sulfate coordinates to a slightly larger extent than calcium.The coordination of sulfate to solute hydroxyl groups seems also to have entropic contributions; in all solvation shells higher coordination at higher temperature was observed.Water has a higher affinity to calcium ions than to sulfate ions.

Single-Stranded Amylose and Cellulose in Ionic Solution.
Figure 4 shows the radii of gyration for the simulations of single-stranded amylose and cellulose.Cellulose's radii of gyration show higher values than single-stranded amylose's.According to that observation, cellulose stays highly elongated during the simulation, whereas single-stranded amylose forms compact structures, which however show sizeable fluctuations.This is reflected in the final structures of the two molecules (Figures 2(e      changed.Radial distribution functions of the two molecules are depicted in Figures 5 and 6.Comparing the coordination of calcium with sulfate, similar behavior in both simulations, of amylose and cellulose, can be observed.Both plots show higher calcium-sulfate affinity at higher temperature.Comparing the coordination of calcium and sulfate ions with solute hydroxyl groups, the two sugars show a rather different temperature dependence: the shapes of the curves in Figures 5 and 6 are similar, but in the case of amylose, ionic cordination is favoured at higher temperature, while in the case of cellulose, at lower temperature.

Discussion
In this work, double-stranded and single-stranded amyloses and single-stranded cellulose have been simulated under various conditions regarding solvent composition, ionic strength, and temperature.In order to observe the role of hydrogen bonds in helix formation and the formation of compact structures of double-stranded amylose, different approaches have been used to disrupt the hydrogen bond network formed by the two strands of amylose.First, the interactions between donor and acceptor atoms have been switched off; in another approach all hydroxy-groups involved in hydrogen bonds have been methylated.
From this study it can be concluded that hydrogen bonds are important for the stability of the amylose doublehelix.Introducing methoxy-groups instead of hydroxygroups hinders the formation of a helix.Changing the solvent from water to DMSO increases interstrand hydrogen bond stability which can be explained by a lack of competition between hydrogen bonds with water molecules and the hydroxy-groups of amylose.At higher temperature doublestranded amylose in calcium sulfate solution shows less interstrand hydrogen bonding and forms more compact structures.Another observation made in this work is that the coordination of calcium with sulfate is entropy-driven, and higher coordination at higher temperatures was found.Also the coordination of ions with the solute hydroxyl groups shows such behavior.
Single-stranded amylose and cellulose are similar molecules that differ in the nature of their linking glycosidic bonds.Cellulose was found to stay in an elongated conformation, whereas single-stranded amylose forms more compact structures.Another striking difference between the two molecules is the sensitivity of the coordination of ions to the solute hydroxyl groups to the temperature.The International Journal of Carbohydrate Chemistry  coordination of calcium and sulfate ions to solute hydroxyl groups seems to be entropy-driven in the case of amylose, whereas in the case of cellulose it is enthalpy dominated.This suggests that entropy considerations cannot be neglected when explaining the structural differences between amyloses and celluloses.

Figure 2 :
Figure 2: Final structures of double-stranded amylose simulated in water (amy dou H 2 O (a), amy met dou H 2 O (b)) and in DMSO (amy dou DMSO (c), amy met dou DMSO (d)), and of single-stranded amylose and cellulose in calcium sulfate solution (amy sin H 2 O caso (e), cel sin H 2 O caso (f)).

International
) and 2(f)).Neither molecule significantly changes its behavior when the temperature is

Figure 3 :
Figure 3: Radial distribution functions for different atom pairs of the simulation of double-stranded amylose in calcium sulfate solution at the two temperatures 278 K (black line) and 313 K (red line).Calcium with sulfate (A), calcium with water oxygen (B), calcium with amylose oxygen O 2 (C), calcium with amylose oxygen O 3 (D), calcium with amylose oxygen O 6 (E), sulfate with water oxygen (F), sulfate with amylose oxygen O 2 (G), sulfate with amylose oxygen O 3 (H), sulfate with amylose oxygen O 6 (I).

Figure 5 :
Figure 5: Radial distribution functions for different atom pairs of the simulation of single-stranded amylose in calcium sulfate solution at the two temperatures 278 K (black line) and 313 K (red line).Calcium with sulfate (a), calcium with water oxygen (b), calcium with amylose oxygen O 2 (c), calcium with amylose oxygen O 3 (d), calcium with amylose oxygen O 6 (e), sulfate with water oxygen (f), sulfate with amylose oxygen O 2 (g), sulfate with amylose oxygen O 3 (h), sulfate with amylose oxygen O 6 (i).

Figure 6 :
Figure 6: Radial distribution functions for different atom pairs of the simulation of cellulose in calcium sulfate solution at the two temperatures 278 K (black line) and 313 K (red line).Calcium with sulfate (a), calcium with water oxygen (b), calcium with cellulose oxygen O 2 (c), calcium with cellulose oxygen O 3 (d), calcium with cellulose oxygen O 6 (e), sulfate with water oxygen (f), sulfate with cellulose oxygen O 2 (g), sulfate with cellulose oxygen O 3 (h), sulfate with cellulose oxygen O 6 (i).

Table 1 :
Overview of the performed MD simulations of the different double-stranded (dou) or single-stranded (sin) carbohydrate systems: amylose (amy) and cellulose (cel).

Table 2 :
Hydrogen bond percentages (>10%) for the simulations of double-stranded amylose in pure water and in DMSO and for methylated molecules as well as for the (alchemical) molecules with excluded hydrogen bond interactions all at 313 K. (molecule number: sugar unit number: atom name).

Table 3 :
Inter-and intramolecular hydrogen bond percentages (>5%) for the simulation of double-stranded amylose in ionic solution at the temperatures 278 K and 313 K. (molecule number: sugar unit number: atom name).
Figure4: Radii of gyration for the ionic solutions of single-stranded amylose and cellulose at the temperatures 278 K and 313 K. Black: amy sin H 2 O caso at 278 K. Red: amy sin H 2 O caso at 313 K. Green: cel sin H 2 O caso at 278 K. Blue: cel sin H 2 O caso at 313 K.