Molecular Dynamics Simulation and NMR Study of Aqueous

position stayed within their respective wells throughout the time courses of the simulations. However, analysis of the hydration water around the ...
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J. Phys. Chem. B 2001, 105, 8629-8638

8629

Molecular Dynamics Simulation and NMR Study of Aqueous Neocarrabiose 41-Sulfate, a Building Block of K-Carrageenan Kazuyoshi Ueda,*,† Mariko Saiki,‡ and John W. Brady§ Department of Material Science, Faculty of Engineering, Yokohama National UniVersity, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan, Department of Chemistry, Faculty of Science, Hiroshima UniVersity, Kagamiyama, Higashi-Hiroshima 739, Japan, and Department of Food Science, Stocking Hall, Cornell UniVersity, Ithaca, New York 14853 ReceiVed: January 29, 2001; In Final Form: May 17, 2001

The solution conformation of neocarrabiose 41-sulfate, which is a building block of κ-carrageenan, was investigated by a combination of molecular dynamics simulations and 1H NMR experiments. The calculated Ramachandran-type potential energy map for the glycosidic torsion angles φ and ψ of this dimer showed that there are two principal minimum-energy conformations, designated here as “a” and “b”. Comparison of the depths of these minima and the MD trajectories started from each minimum indicated that in a vacuum the molecular conformation in the “a” well is more stable than that in the “b” well. On the other hand, MD simulations in water showed that trajectories started from each minimum position stayed within their respective wells throughout the time courses of the simulations. However, analysis of the hydration water around the molecule indicated that the stability of the molecular conformation in the “a” well would be favored by solvation compared to the “b” well. Analysis of the experimental NOE-NMR data using the above computational results strongly indicated that the conformation in the “a” well is the only stable one in water for neocarrabiose 41-sulfate. This conformation is very similar to that reported by X-ray diffraction experiment for ι-carrageenan fiber, although the molecular size and the experimental conditions are different between the two cases.

Introduction Carrageenans are widely used in the food industry because of their ability to form gels.1 However, the details of the mechanism of gel formation are still a matter of debate.2-8 To clarify this problem, many studies have been done using a variety of techniques, such as X-ray diffraction,2,5 optical rotation,3,9-12 NMR13-15 and IR16,17 spectroscopies, electron microscopy,18 and light scattering.19-23 The three-dimensional structure of this polysaccharide in water is of primary importance to understanding the gel formation mechanism at the atomic level. To obtain information about the properties of carrageenan in water, we have been investigating the conformational behavior of the dimer and oligomer fractions of carrageenan in water using molecular dynamics (MD) simulations. Compared to the tremendous amount of experimental work for carrageenan polymers, reported computer simulation studies are still relatively few in number.24-32 In our previous studies of the disaccharide repeat units of β-carrageenan (neocarrabiose and carrabiose), which have no sulfate groups in their structures, it was found that hydration can have a large effect to the conformations of these disaccharides in water.31,33 Although β-carrageenan has the most basic structure among the carrageenan family, the most common type of carrageenan is κ-carrageenan, which has one sulfate group at the C4 position of the β-D-galactopyranose residues. It might be expected that such an ionic functional group would significantly affect the

conformation of the molecule containing it and the water structuring around it. As part of a series of studies of molecules belonging to the carrageenan family, the present study investigated neocarrabiose 41-sulfate, a building block of κ-carrageenan, using molecular mechanics (MM) calculations, MD simulations, and 1H NMR experiments. The effects of the sulfate group on the conformation of the disaccharide and the structuring of the adjacent solvent will be discussed by comparison with our previous results for unsulfated neocarrabiose. It was found that the addition of the sulfate group to the neocarrabiose molecule changed the shape of the potential energy map dramatically through the electrostatic interactions between the partial charges on each atom of the neocarrabiose molecule and the electric charge of the sulfate residue. These electrostatic interactions were found to restrict the allowed area of φ and ψ in the Ramachandran energy map to two distinct, narrow areas. The global minimum for (φ, ψ) is around (-172°, -168°), which was close to the experimental values of the dihedral angles for ι-carrageenan found using X-ray fiber diffraction.34 The other minimum is at (-83°, 64°) and is 1.0 kcal/mol higher in energy than the global minimum. Although the energy difference between these two wells is comparable to thermal energy fluctuations at room temperature, the combination of the simulation results and the NMR-NOE data show that for neocarrabiose 41-sulfate in water only the conformational well at (-172°, -168°) is populated to any appreciable extent. Experimental Procedures

* To whom correspondence should be addressed. † Department of Material Science. ‡ Department of Chemistry. § Department of Food Science.

Parametrization. All MM and MD calculations were performed using the CHARMM25 program.35 The force field parameters used were those developed by Ha et al. for

10.1021/jp0103631 CCC: $20.00 © 2001 American Chemical Society Published on Web 08/17/2001

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Ueda et al. TABLE 1: Partial Atomic Charges and Force Parameters for Sulfuric Residue: Atom Notations Shown in Figure 2a (a) Partial Charge atom

atom type

charge

H4′ C4′ O4′ S1′ OS1′ OS2′ OS3′

H C OS SO4 OS4 OS4 OS4

0.10 0.04 -0.45 1.35 -0.68 -0.68 -0.68

(0.31) (0.0) (0.0) (0.0)

(b) Bond bond type

kb (kcal/mol Å2)

b0 (Å)

SO4-OS SO4-OS4 OS-C

239.7 518.0 330.3

1.63 1.44 1.40

(c) Bond Angles angle type

kθ (kcal/mol rad2)

θ0 (deg)

C-OS-SO4 OS-SO4-OS4 OS4-SO4-OS4 H-C-OS C-C-OS

54.0 122.4 153.9 45.2 81.0

116.1 101.8 115.3 107.2 109.4

(d) Dihedral Angles

Figure 1. Comparison of the CHARMM (0) and ab initio (O) potential energy curves of the C-C-O-S dihedral angle rotation for the monoethyl sulfate molecule (a) and for the monoisopropyl sulfate molecule (b). The angles were measured from the cis position.

carbohydrate molecules.36 Since parameters for sulfate groups are not included in this force field, these parameters were derived for the present study by fitting the potential energy curves obtained from an ab initio SCF calculation to the CHARMM force field functions by using a nonlinear least-squares method.37 Although some of the parameters for the sulfate group have appeared previously in the literature,38-41 MM parameters need to be consistent for the whole parameter set used. Therefore, the parameters for the sulfate group were separately derived in the present study by taking into account the results of previous work for different parameter sets. The functional form of the typical CHARMM force field used is given in eq 1 of ref 36. Ab initio calculations were performed using the GAUSSIAN 94 program with an RHF 6-31G* basis set.42 To obtain force constants for the bond lengths, bond angles, and dihedral angles of -O-SO3-, monomethyl sulfate, monoethyl sulfate, and monoisopropyl sulfate were used as model molecules. Each model molecule was first fully optimized to obtain the lowest energy conformation. The optimized structures were then successively varied in their bond lengths, bond angles, and dihedral angles from the optimized values and the single point potential energies of the distorted conformations were calculated. Each conformational parameter was varied until the calculated energy of the distorted conformation reached approximately 10 kcal/mol above from that of the optimized state. The values of the potential energy for bond length were calculated for every 0.02 Å increment from the equilibrium bond length r0, and bond angles were increased in increments of 5.0° from the equilibrium angle θ0. Dihedral angles were rotated in increments of 30° in both directions from the cis position of a selected C-C-O-S dihedral linkage in the interval [+180°, -180°]. In the above calculation, only one structural parameter was changed at a time

angle type

kφ (kcal/mol)

n

phase

X-OS-SO4-X C-C-OS-SO4 C-C-OS-SO4 C-C-OS-SO4

0.214 -1.728 0.496 -0.229

3 1 3 5

0.0 0.0 0.0 0.0

a

The values in the parenthesis are reduced charges, see text in detail.

and the other parameters for bond lengths, bond angles, and dihedral angles were kept fixed at their optimized positions. The parameters were iteratively adjusted in order to satisfy all model molecules simultaneously. The partial charges were calculated using GAUSSIAN94 with the Merz-Singh-Kollman method43,44 for the molecule of β-D-galactopyranose 4-sulfate. In this parametrization, a dielectric constant of 1 was used, consistent with the remainder of the carbohydrate force field used here.36 Typical examples of the comparison between the ab initio and the CHARMM potential energy curves for the dihedral angles are shown in Figure 1a,b. These figures show the potential energies for the molecules monoethyl sulfate and monoisopropyl sulfate, respectively, for changes of the dihedral angle C-C-O-S, calculated using the same dihedral force field parameters. The characteristic features of the potential energy curves for both molecules can be well represented by the new parameters. Since force constants derived from ab initio calculations for bonds and angles are known to have values 1015% higher than experimental values, the fitted values were scaled by a factor of 0.9, following Woods et al.45 Force constants obtained for all residues are listed in Table 1. These parameters were tested by comparing the energy-minimized conformation of the 4-sulfated β-D-galactose molecule with that obtained by ab initio calculation, and the results are shown in the section of Supporting Information as Table 1S. The agreement between these two calculations is good for all conformational parameters. Calculation. The present calculations were generally performed in the same manner as those previously reported for neocarrabiose.31 In brief, the starting structure for the neocarrabiose 41-sulfate disaccharide was taken from the conformation of the double-helical ι-carrageenan structure proposed from

Aqueous Neocarrabiose 41-Sulfate

J. Phys. Chem. B, Vol. 105, No. 36, 2001 8631

Figure 2. Structure and nomenclature of neocarrabiose 41-sulfate.

X-ray fiber diffraction.34 This structure was modified by replacing the sulfate group on the C2 carbon of the nonreducing ring with a hydroxyl group. A schematic illustration of neocarrabiose 41-sulfate and its nomenclature are shown in Figure 2. The glycosidic linkage dihedral angles φ and ψ are defined as C2-C1-O1-C3′ and C1-O1-C3′-C2′, respectively, in accordance with our previous definition.31) These definitions can be transformed to the IUPAC-IUB recommended dihedral definitions through the following equations: φ(O5) ) φ - 120, ψ(C4′) ) ψ - 120, where φ(O5) ) O5-C1-O1-C3′ and ψ(C4′) ) C1-O1-C3′-C4′, and φ(H1) ) φ + 120, ψ(H3′) ) ψ + 120, where φ(H1) ) H1-C1-O1-C3′ and ψ(H3′) ) C1-O1-C3′-H3′. A Ramachandran-like adiabatic conformational energy map46 for this disaccharide was prepared using the same minimization-search approach employed in the previous paper, which consisted of several stages.31 MD trajectories were integrated using a Verlet integrator with a time step of 1 fs.47 Bond lengths involving hydrogen atoms were kept fixed by using the SHAKE constraint algorithm.48 The trajectories in a vacuum were started at 60 K and heated in increments of 60 K at 2 ps intervals until a temperature of 300 K was reached. These trajectories were then equilibrated at 300 K for 10 ps followed by 500 ps of additional simulation which was used for analysis. The trajectories in water were calculated using a periodic cubic box of length 24.62 Å. The disaccharide was placed at the center of the box surrounded by 484 TIP3P water molecules.49 One sodium ion was placed in the box as a counterion at a position about 3 Å away from the sulfate group as an initial, starting position. No additional salts were included in this model. The density and weight concentration of the resulting solution are 1.017 g/cm3 and 4.66%, respectively. Cubic periodic boundary conditions were imposed in all directions. Long-range interactions were tapered to zero by applying a switching function between 10.0 and 12.0 Å on a neutral group basis.50 All electrostatic interactions were calculated using the Ewald summation scheme.51 The trajectories in water were first equilibrated at 300 K for 20 ps, followed by 180 ps of dynamics used for data collection. NMR Experiment and Sample Preparation. A sample of Neocarrabiose 41-sulfate (Lot No. 95F-0314) was purchased from Sigma Co. Ltd. and used without further purification. This sample was dried overnight under reduced pressure prior to the preparation of the solution. A concentration of 22 g L-1 in D2O was used for NMR measurement. All NMR spectra were recorded on a JEOL GXS500 spectrometer using the standard pulse sequences supplied by the instrument manufacturer. 2DCOSY and NOESY spectra were recorded with a 3050 Hz spectral width in both dimensions and 1024 data points in f2 and 256 data points in f1 with 16 scans at each increment. Twodimensional NOESY experiments were measured with variable

Figure 3. The adiabatic potential energy surfaces for neocarrabiose 41-sulfate. (a) The surface calculated with full charges for the sulfate residue. (b) The potential energy surface which was calculated by using a model whose partial charges of sulfuric residue were reduced to nearly zero. Contours are in 2 kcal/mol intervals.

mixing times of 500, 750, and 1000 ms. A mixing time of 750 ms was found to give the best resolution of signals. Proton chemical shifts were referenced to the external tetramethylsilane. Results and Discussion Conformational Energy Map. Figure 3a shows the vacuum adiabatic conformational energy map for neocarrabiose 41sulfate. This relaxed energy map exhibits two major local minima, labeled “a” and “b”. The minimum dihedral angles of “a” and “b”, and their potential energy differences are listed in Table 2 with other characteristic conformational information. The global minimum is in the “a” well at (φ, ψ) ) (-172°, -168°). This position is in good agreement with the global minimum positions calculated for neocarrabiose 41-sulfate by Urbani et al.26 and Le Questel et al.29 The former used a rigidly constrained model for sugar residues and the latter used the Tripos force field with no electrostatic contributions. However, the features of the other potential wells are different between Figure 3a and the potential map of Le Questel et al.29 Their map is basically the same as our previously obtained map for neocarrabiose,31 with at least three principal minima while in our new map for neocarrabiose 41-sulfate, the number of minima

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Figure 4. Variation of the relative potential energy with the amount of charge of the sulfate residue. The curves were calculated for the conformation “c” (0) and “e” (4), respectively.

TABLE 2: Summary of the Characteristic Features of the Local Minimum-Energy Structures from the Calculated Adiabatic Energy Surface for Neocarrabiose 41-Sulfate, Obtained for Full Charge and Reduced Charge Calculations for Sulfuric Residue

structure (full charge) a b (reduced charge) c d e f

interring primary potential hydrogen alcohol energy φ ψ (deg) (deg) (kcal/mol) conformation bonds -172 -168 -83 64 83 -140 -57 174 -87

-64 179 49

0 1.0

TG TG

none O2-HO2 to O2′

0

TG

2.9 4.3 6.4

TG TG TG

O2-HO2 to O2′ none none O2-HO2 to O2′

is reduced to only two broad wells. This seems to indicate that the conformation of the neocarrabiose is restricted by the sulfate group on the C4 position of the β-D-galactopyranose ring. To confirm the effect of the addition of a sulfate group on the neocarrabiose molecule, we divide it into two factors: the increment of the electrostatic interaction due to the addition of the negative charge and steric effects due to the addition of a bulky group. To clarify the main factor contributing to the difference in the shape of the map, the total value of the partial atomic charges for the sulfate group was reduced from -1 to zero and the Ramachandran map was recalculated by the same procedures above. The reduced values of the partial charge for each atom of the sulfate used in this calculation are listed in Table 1 in parentheses. The calculated map for the reduced charges is shown in Figure 3b. The dihedral angles and the relative energies of the minima “c-f” are summarized in Table 2. Although the contour surface of the map is different from Figure 3a, it is very similar to that of the previously calculated map for neocarrabiose. In the previous map for neocarrabiose, the global minimum position is at (81°, -141°). This is the same as the global minimum value on the present map at “c” in Figure 3b. Other wells are also in similar positions in both maps. This congruence indicates that the changes of the shape of the adiabatic map shown in Figure 3a are mainly due to the electrostatic interactions of the sulfate group, and that steric clashes do not influence the basic shape of the potential energy map. The most remarkable difference between these figures is the shift of the global minimum position from “c” to “a”. On the

Figure 5. Typical trajectories of the (φ, ψ) glycosidic linkage angles in a vacuum superimposed on the adiabatic potential energy map. Trajectories were started from the “a” conformation (a) and “b” conformation (b), respectively.

present maps, the position “a” of Figure 3a for the sulfated disaccharide corresponds to position “e” in Figure 3b. To investigate this shift in more detail, the charge of the sulfate group was incrementally changed from zero to -1 in 0.2 increments and the potential energy of the whole molecule was compared for both conformations “c” and “e” at each charged state. The results are shown in Figure 4, where the potential energies are plotted as relative energies measured from the lowest energy value at the conformation “e” with -1 charge. Although the potential energy of the conformation “c” is lower than that of “e” when the charge of the sulfate group is zero, the energy of “e” decreases rapidly with the increment of the charge, with the ordering of the energies of “e” and “c” reversing at a charge of around -0.5. This result indicates that the larger the negative charge of the sulfate group, the more stable conformation “e” is. Although conformation “e” is more stable than “c” for the full -1 charge, Figure 4 indicates that its stability should depend strongly on the magnitude of the electrostatic interactions. In solution, the strength of the electrostatic interaction is greatly affected by the surrounding solvent. In particular, the water molecules around the disaccharide molecule should affect the strength of the electrostatic interactions and thus the conformation of this molecule. The other characteristic feature of the map shown in Figure 3a is the appearance of the “b” well. Although this well does

Aqueous Neocarrabiose 41-Sulfate

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Figure 7. Typical trajectories of the (φ, ψ) glycosidic dihedral angles in water superimposed on the adiabatic energy map for simulations which started from the “a” and “b” conformations, respectively.

Figure 6. History of the glycosidic dihedral angles φ (a) and ψ (b) in the vacuum simulation which was started from “b” conformation.

not appear on the map of Le Questel et al.,29 it corresponds to the N8-well (centered at (-100°, 40°) using our dihedral notation) obtained for the neocarrabiose map of Lamba et al.24 The same well was also found to be a quasi-stable minimum in our previous map for neocarrabiose. Although this “b” well was not important for the neocarrabiose molecule, the addition of the sulfate residue enhanced the importance of this well by increasing its relative depth in the neocarrabiose 41-sulfate case. To check the energy difference between the “a” and “b” conformations, semiempirical energy calculation were also performed using MOPAC PM3. The result showed that the energy difference was 1.6 kcal/mol, which is quite similar to the value obtained in Table 2. However, It can be expected that the “b” well would become less important in an aqueous environment as the potential energy of “f” become larger than others in Figure 3b. Vacuum Simulations. Molecular dynamics trajectories for neocarrabiose 41-sulfate were calculated in a vacuum at 300 K to determine whether the calculated energy surface adequately represents the dynamical behavior of the molecule. The trajectories were started from points “a” and “b” of Figure 3a. For each starting point, six independent trajectories were calculated by assigning different initial velocities for each atom. These trajectories were found to exhibit very similar behavior. Typical examples of (φ, ψ) trajectories which started from the “a” and “b” positions are shown in Figure 5a,b. Both trajectories are well confined by the low-energy region of the surface, which indicates that the shape of the potential surface is correct. The trajectory which started from the “a” position stayed in the same well for the entire 500 ps period of the calculation. On the other hand, the trajectories which were started from the “b” position underwent transitions from the “b” to the lower-energy “a” well. To better illustrate the transition behavior, the time courses of φ and ψ for a typical “b” trajectory are shown in Figure 6a and b, respectively. As can be seen the molecule stayed in the “b” well for the first 35 ps, but soon moved toward the “a” well and never returned to the “b” well. The other 5 trajectories also

showed similar behavior, since the conformation of neocarrabiose 41-sulfate in the “a” well is more stable than that of the “b” well in a vacuum. Solution Simulations. The molecular motion in aqueous solution was also modeled and typical trajectories of the glycosidic linkages (φ, ψ) are shown in Figure 7. In this figure, two trajectories which were started from the “a” and “b” wells were superimposed on the same adiabatic potential energy map simultaneously. Although the trajectory which started from the “a” position stayed within that same well for the entire simulation as in the vacuum simulation, the shape of the area traced out was somewhat different from those of the vacuum trajectories as the molecule made occasional excursions to higher energy regions of the adiabatic potential map. These fluctuations can be attributed to the solvation effects of the water. However, the effects on the average conformation are not drastic and the trajectory returned and stayed in the same well even after the large excursion out of the well. The individual time courses of φ and ψ for the trajectory which started from the “a” well are shown in Figure 8. It can be seen that the range of the motion sampled by φ and ψ increased in water compared to that in a vacuum.52 As can be seen, the angle φ reaches values around -100° several times. The averages of φ and ψ for the entire time courses of these trajectories were -176° (root mean square (rms) fluctuation of 11.8°) and -160° (rms fluctuation of 18.1°), respectively. While the fluctuations of the glycosidic dihedral increased due to hydration, both trajectories remained in the well in which they began throughout the time period investigated, implying stability for this molecule in this conformation. This stability appears to be explained by the favorable electrostatic interaction energy introduced by the addition of the sulfate residue on the β-D-galactopyranose ring of neocarrabiose. In such electrostatic interactions, the presence of the counterion should play an important role because the strong binding of the counterion to the sulfate group would reduce the extent of such interaction. The time course of the distance between the Na+ and sulfar atom was investigated, and the results are shown in Figure 9. At the beginning, the distance was around the starting distance of from 3 to 4 Å, but gradually increased to around 6 Å, and then suddenly increased to 14 Å at 100 ps. As can be seen the hydrated counterion can move around freely in the water without being bound closely to the sulfate residue. Thus, the counterion does not directly cancel the charge of the

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Figure 8. History of the glycosidic dihedral angles φ (a) and ψ (b) in the water simulation which was started from the “a” conformation.

Figure 9. The time course of the distance between the counterion Na+ and sulfar atom of the sulfuric residue of the neocarrabiose 41-sulfate in water.

sulfate residue and the electrostatic force of the sulfate residue can strongly affect the conformation of the disaccharide as was seen in Figure 4. Because the conformational transition of carrageenan polymer is known to depend on the species of counterion and the concentration of added salts, these effects will be investigated in our oligomer model of carrageenan in a future study. A trajectory which began in the “b” well also remained in this same well throughout the time simulated. This stability is different from the behavior of the trajectory in a vacuum, where the molecule moved toward the global minimum on the vacuum surface at “a”. This solution trajectory seems to indicate the existence of a relatively stable conformation at “b” in an aqueous environment. However, it is not possible to determine the relative stability of these two wells in water from the present simulations because there were no transitions between these two conformations. It was not feasible to extend these simulations to time scales long enough to allow multiple transitions between wells. This problem could be addressed by calculating a potential of mean force for the transition using umbrella sampling.53,54 We plan to attempt the calculation of such a map for this molecule in the near future.

Figure 10. Stereoscopic view of a snapshot of the neocarrabiose 41sulfate in water from the trajectory started from the “a” conformation. Three water molecules made hydrogen bond bridges between the O2O2′ hydroxyl oxygens, the O2-sulfate oxygens, and the O6-sulfate oxygens, respectively.

From the present data the relative stability of these two conformers “a” and “b” can be examined further by considering the interaction of the solvent with these two conformations. In our previous study of neocarrabiose, hydrogen bonding to water was found to play an important role in the determination of the most stable conformation in solution.31 In that molecule two hydroxyl groups on different sugar rings were found to be directly hydrogen bonded with each other in the vacuum conformation. However, in solution a water molecule inserted between them and broke their direct hydrogen bond and instead made a hydrogen bond bridge between these two hydroxyl groups. This water insertion produced a conformational shift in neocarrabiose. Similar to the previous work, water bridges were also found in this study in the solution trajectories of both the “a “ and “b” conformations. These water bridges were formed between the O2 and O2′, O2 and O4′, and O5 and O2′ atom pairs. The percentages of the total trajectory times that these bridges exist are shown in Table 3. The number of

Aqueous Neocarrabiose 41-Sulfate

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TABLE 3: Comparison of the Percentage of the Interresidue Water Bridges Occurring in the Solution Trajectories Started from “a” Well and “b” Well, Respectively percentage of the total trajectory time during which each water bridge occurred water bridge

“a” well

“b” well

O2-O2′ O2-O4′ O5-O2′ O2-OS*′ O5-OS*′ O6-OS*′ O6′-OS*′ a

65.4 11.4 31.2 32.0 0.0 5.8 45.0

28.9 0.0 0.5 0.0 47.2 12.1 42.6

a

This is not an interresidue but an intraresidue water bridge.

hydrogen bonds were calculated using a geometric definition which required an oxygen-oxygen distance of less than 3.5 Å and a donor oxygen-hydrogen-acceptor oxygen angle of greater than 120°.52 It can be seen that the most common type of water bridges in both trajectories started from either the “a” or “b” conformations were those between O2 and O2′. Most of the water bridges found in the “a” conformation were the same type which was found in the neocarrabiose in water. That is, a water bound to the oxygen which was one of the hydroxyl groups of O2 and O2′, and the same water oxygen bound to a hydrogen which belongs to the other hydroxyl group of O2 and O2′. In the neocarrabiose case studied previously, this bridging water molecule stabilized the disaccharide conformation at around φ ) 180° and ψ ) -166°. These average values of the dihedral angles φ and ψ in water are almost same as for the “a” conformation on the neocarrabiose 41-sulfate energy surface. A typical snapshot of the structure of such a water bridge is shown in Figure 10 along with other types of water bridges.

This type of water bridge was present during 65% of the total simulation time. Since the “a” structure is the most stable conformation for neocarrabiose 41-sulfate even in a vacuum, without water, the water bridge would further enhance the stability of this conformation in aqueous solution. A similar water bridge between O2 and O2′ was also found in the trajectory which began from the “b” well in solution. However, the percentage of time that this hydrogen bond was present was only 29% of the total simulation, which is less than half of the time such a hydrogen bond was observed in the simulation which started from the “a” well. Instead, a direct hydrogen bond between O2 and O2′ was found to form for 63% of the total simulation time in the trajectory which started from the “b” well. This type of direct hydrogen bond would be weakened and easily broken by the attack of water molecules which could insert between them. The breaking of the intramolecular hydrogen bond should destabilize the “b” conformation and would be expected to cause a conformational shift to the “a” conformation which is more stabilized by hydration. Bosco et al.32,55 have measured the NMR-NOE signals of κ-carrageenan oligomer and have suggested the existence of water bridges between the neocarrabiose 41-sulfate units. They have suggested that these bridges are mainly formed between the O2 and sulfate oxygens and between the O6′ and sulfate oxygens. They also proposed that the stabilization of the helical structure of a carrageenan polymer would be enforced by these water bridges. Our simulation in water shows that both the O2 and O6′ hydroxyl groups made hydrogen bond bridges with sulfate oxygens via water molecules for substantial portions (32% and 45% respectively) of the simulation of the “a” well conformation as shown in Table 3. Bosco et al.32 also indicated that the hydroxyl groups O2-HO2 and O6′-HO6′ serve as donors in the bridging hydrogen bonds to the sulfate at position

Figure 11. 1H NMR spectrum of neocarrabiose 41-sulfate. The characters R and β indicate the signals which came from the equilibrium of the R and β anomers, respectively.

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TABLE 4: Average Number of Hydrogen Bonds to Solvent Made by Each Sugar Oxygen Atom and Sulfuric Residue Oxygen Atoma no. of hydrogen bonds atom

“a” well

“b” well

(difference)

O1 O2 O4 O5 O6 O1′ O2′ O4′ O5′ O6′ sub total OS1′ OS2′ OS3′ total

1.20 2.77 2.69 0.80 1.01 2.85 2.74 1.10 0.91 2.54 18.6 1.96 2.62 2.21 25.4

1.22 2.30 2.72 1.38 1.06 2.72 2.10 0.81 0.92 2.59 17.8 2.30 2.39 2.21 24.7

(-0.02) (0.47) (-0.03) (-0.58) (-0.05) (0.13) (0.64) (0.29) (-0.01) (-0.05) (-0.34) (0.23) (0.00)

a Calculated from the solution trajectory using geometric criteria, with a distance cutoff of 3.5 Å and an O-H-O angle cutoff of 120˚

4. In our simulation, the hydrogen of the O2 hydroxyl group mainly serves as a donor with the hydrogen bonded water in the water bridge conformation between O2 and the sulfate oxygens. This situation is also in agreement with the experimental results. The O6′-HO6′ hydroxyl group serves as both donor and acceptor depending on the rotation of the sulfate group and the O6′-HO6′ hydroxyl group in our simulation. Irrespective of the nature of the hydrogen bonding, the sulfate group and the O6′-HO6′ hydroxyl group is hydrogen bonded via a bridging water molecule for a substantial proportion of the trajectory. For the water bridge between O2 and O2′, the hydrogen of HO2′ mostly plays as a donor to the bridging water

oxygen and the oxygen of O2 mostly serves as an acceptor to the water hydrogen. This result again indicates that the agreement between the NMR experiment and molecular simulation in water is quite good. Table 4 shows the average number of hydrogen bonds which were formed between solvent water molecules and the solute neocarrabiose 41-sulfate. It was found that the total number of hydrogen bonds in the “a” conformation was a little larger than for the “b” conformation. This implies that the “a” conformation would be more stabilized by these hydrogen bonds than the “b” conformation. The number of hydrogen bonds for individual oxygen atoms also differs between these two wells, with more bonds at the O2 and O2′ positions in the “a” conformation compared to the “b” conformation. In summary, in water the “a” conformation is more stable than the “b” conformation. Although no transitions from the “b” well to the “a” conformation were observed in this trajectory, presumably because of the limited length of the calculation, the potential energy difference and hydration analysis results suggest that the “a” conformation would be the most favored conformer in water. NMR Experiment. To determine the conformation of neocarrabiose 41-sulfate in water, 1H NMR spectroscopy was measured at 25 °C in D2O. Figure 11 shows the one-dimensional 1H NMR spectrum of neocarrabiose 41-sulfate, illustrating the complex signal which comes from the equilibrium of the R and β-anomers of the D-galactopyranose ring. The signals were assigned using the 2D-COSY cross peaks and 13C-1H heteronuclear correlated spectra. The assignments and their chemical shifts are summarized in Table 5 for the β-anomer. To obtain distance information between aliphatic protons, the 2D-NOESY spectrum was measured and the results are shown in Figure 12. The 2D-NOESY spectrum shows several intraresidue and interresidue NOE contacts between aliphatic protons. Large

Figure 12. NOESY spectrum in D2O of neocarrabiose 41-sulfate. Relevant cross peaks are indicated as cross points of dashed lines.

Aqueous Neocarrabiose 41-Sulfate

J. Phys. Chem. B, Vol. 105, No. 36, 2001 8637

TABLE 5: 1H NMR Chemical Shifts of Neocarrabiose 41-Sulfate residue

proton

chemical shift (ppm)

3,6-anhydro-R-D-galactose

H1 H2 H3 H4 H5 H62 H61 H1′ H2′ H3′ H4′ H5′ H61′, H62′

4.89 3.90 4.15 4.27 4.20 3.99 3.82 4.44 3.39 3.76 4.63 3.53 3.58

β-D-galactose

interresidue NOE signals were found between H1-βH4′ and H1-βH3′. Analysis of the energy-minimized conformation of neocarrabiose 41-sulfate in the “a” well indicated that the closest distance between interresidue aliphatic protons is the H1-βH4′ pair (2.10 Å), and the next nearest pair is H1-βH3′ (2.89 Å). Since the conformation of the thermalized molecule fluctuates in water, the above distances should be evaluated as trajectory averages over the time course of the simulation. These averaged values were 2.30 and 2.83 Å for the H1-βH4′ and H1-βH3′ pairs, respectively. These average distances are consistent with those obtained by NOE experiment. On the other hand, the model analysis of the “b” conformation indicated that the closest interresidue aliphatic proton distance is H2-βH2′ (2.10 Å) and next nearest is H1-βH2′ (2.89 Å). However, NOE signals corresponding to these aliphatic proton distances do not appear in Figure 12. These results show that the neocarrabiose 41-sulfate molecules exist in the “a” conformation. The NMR studies of carrageenan reported by Bosco et al.32 showed strong signals between H1-βH4′ and H1-βH3′. These data indicate that the neocarrabiose 41-sulfate unit has the same structure in both the polymer and dimer molecules in water. Lamba et al. also measured the NOE signal of neocarrabiose in water,24 and they observed a large NOE between H1 and H3′. This is similar to our observation for neocarrabiose 41-sulfate. This indicates that both molecules exist in very similar conformations in water, irrespective of the difference in charge added by the sulfate residue in neocarrabiose 41-sulfate. Conclusions A Ramachandran-type potential energy map for the (φ, ψ) glycosidic dihedral angles of neocarrabiose 41-sulfate was obtained using molecular mechanics calculations. The map showed two large minima, located at ( -172°, -168°), which was denoted as “a”, and the other at (-83, 64), denoted as “b”. The potential energy of the molecule in the “a” conformation is only 1.0 kcal/mol higher than that of the “b” conformation. The molecular dynamics trajectories in water started from each well stayed within the same well throughout the simulation. Therefore, molecular dynamics simulations alone could not determine the relative probabilities of these two wells in water, although the analysis of the hydration around the molecule in each conformation suggested the predominance of the “a” conformation. Analysis of the NMR-NOE experiments coupled with the results of the molecular dynamics simulations clearly showed that the NOE signals coincided with the distances found for the “a” conformation. Signals corresponding to the “b” conformation or a mixture of the “a” and “b” conformers were not be observed in the NOE experiment. The conclusion of this work is that the neocarrabiose 41-sulfate exists in water in the

“a” conformation. The values of the dihedral angles in this well are the same as those obtained for i-carrageenan gel by X-ray fiber diffraction experiment. These studies were done for the dimer molecule at room temperature and with no added salt. Under these conditions, carrageenan polymer exists in a nongel form. Even under these conditions, neocarrabiose 41-sulfate adopts similar dihedral angles as in the gel form. This indicates that carrageenan has similar dihedral angles in both the sol and gel states. Our previous light-scattering measurements showed that carrageenan with a short molecular length adopts a rather elongated conformation in the sol state. Moreover, the conformational change from the sol to gel states was not accompanied by a drastic change of the molecular dimension. This suggested that the dihedral angles of the glycosidic linkages in the neocarrabiose repeat units in the carrageenan chain would be very similar in both the sol and gel states.21 The modeling and NMR experiment in this study were performed on a disaccharide molecule and the further work on longer oligomers would be beneficial to a more complete understanding of the conformational behavior of the polymer. Supporting Information Available: Comparison between energy minimized geometries of 4-sulfated β-D-galactose by GAUSSIAN94 and CHARMM. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Kennedy, J. F. Carbohydrate Chemistry; Clarendon Press: Oxford, 1988. (2) Anderson, N. S.; Campbell, J. W.; Harding, M. M.; Rees, D. A.; Samuel, J. W. B. J. Mol. Biol. 1969, 45, 85-99. (3) McKinnon, A. A.; Rees, D. A.; Williamson, F. B. Chem. Commun. 1969, 701-702. (4) Smidsrod, O.; Grasdalen, H. Carbohyd. Polym. 1982, 2, 270-272. (5) Millane, R. P.; Chandrasekaran, R.; Arnott, S.; Dea, I. C. M. Carbohydr. Res. 1988, 182, 1-17. (6) Snoeren, T. H. M.; Payens, T. A. J. Biochim. Biophys. Acta 1976, 437, 264-272. (7) Paoletti, S.; Smidsrod, O.; Grasdalen, H. Biopolymers 1984, 23, 1771-1794. (8) Hjerde, T.; Smidsrod, O.; Christensen, B. E. Carbohydr. Res. 1996, 288, 175-187. (9) Morris, E. R.; Rees, D. A.; Robinson, G. J. Mol. Biol. 1980, 138, 349-362. (10) Rinaudo, M.; Karimian, A.; Milas, M. Biopolymers 1979, 18, 16731683. (11) Rochas, C.; Rinaudo, M. Biopolymers 1984, 23, 735-745. (12) Austen, K. R. J.; Goodall, D. M.; Norton, I. T. Carbohydr. Res. 1985, 140, 251-262. (13) Rochas, C.; Rinaudo, M.; Vincendon, M. Int. J. Biol. Macromol. 1983, 5, 111-115. (14) Tokita, M.; Ikura, M.; Hikichi, K. Polymer 1989, 30, 693-697. (15) Knutsen, S.; Grasdalen, H. Carbohydr. Res. 1992, 229, 233-244. (16) Belton, P. S.; Wilson, R. H.; Chenery, D. H. Int. J. Biol. Macromol. 1986, 8, 247-251. (17) Belton, P. S.; Goodfellow, B. J.; Wilson, R. H. Macromolecules 1989, 22, 1636-1642. (18) Hermansson, A. Carbohydr. Polym. 1989, 10, 163-181. (19) Viebke, C.; Borgstrom, J.; Piculell, L. Carbohydr. Polym. 1995, 27, 145-154. (20) Slootmaekers, D.; Mandel, M.; Reynaers, H. Int. J. Biol. Macromol. 1991, 13, 17-25. (21) Ueda, K.; Itoh, M.; Matsuzaki, Y.; Ochiai, H.; Imamura, A. Macromolecules 1998, 31, 675-680. (22) Bongaerts, K.; Reynaers, H.; Zanetti, F.; Paoletti, S. Macromolecules 1999, 32, 675-682. (23) Bongaerts, K.; Reynaers, H.; Zanetti, F.; Paoletti, S. Macromolecules 1999, 32, 683-689. (24) Lamba, D.; Segre, A. L.; Glover, S.; Mackie, W.; Sheldrick, B.; Perez, S. Carbohydr. Res. 1990, 208, 215-230. (25) Tvaroska, I.; Rochas, C.; Taravel, F.-R.; Turquois, T. Biopolymers 1992, 32, 551-560. (26) Urbani, R.; Di Blas, A.; Cesaro, A. Int. J. Biol. Macromol. 1993, 15, 24-29.

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