Disaccharide Conformational Flexibility. 11. Molecular Dynamics Simulations of Sucrose V. H. T R A N * and J. W. BRADYt

DPpartmvnt of Food Science, Cornell University, Ithaca, New York 14853

SY NOPSlS

Molecular dynamics simulations have been used to study the motions in vacuum of the disaccharide sucrose. Ensembles of trajectories were calculated for each of the five local minimum energy conformations identified in the adiabatic conformational energy mapping of this molecule. The model sucrose molecules were found to exhibit a variety of motions, although the global minimum energy conformation was found to be dynamically stable, and no transitions away from this structure were observed to occur spontaneously. In all but one of these vacuum trajectories, the intramolecular hydrogen bond between residues was maintained, in accord with recent nmr studies of this molecule in aqueous solution. Considerable flexibility of the furanoid ring was found in the trajectories. No "flips" to the opposite puckering for this ring were found in the simulations starting from the global minimum, although such a transition w a s observed for a trajectory initiated with one of the higher local minimum energy conformations. Overall, the observed structural fluctuations were consistent with the experimental picture of sucrose as a relatively rigid molecule.

INTRODUCTION One of the most powerful means of analyzing biopolymer dynamics has been through the use of theoretical simulation methods. Theoretical modeling studies are often capable of revealing information about dynamics on the molecular level that is difficult or impossible to obtain by other means. Molecular dynamics simulations, in which the equations of motion of a molecular system responding to a molecular mechanics force field are simulated directly, have now been used successfully for a number of years in the study of a variety of physical systems, including bi~polymers.'-~However, such dynamics simulations of saccharides have lagged behind those of polypeptides, proteins, and

1990 John Wiley & Sons, Inc. CCC o(M,e;-.~a25/90j050977-21 $04.00 Biopolymers, Vol. 29, 977-997 (1990) *Permanent address: Laboratoire de Physicochimie des Macromolerules, lnstitut National d e la Recherche Agronomique, H.P. 527, 44026 Nantes Cedex 03, France. '7'0 u hotri correspondence should be addressed.

nucleic acids. Recently, studies of the hexa-NAG substrate of l y ~ o z y m e ~i-D-glucose,~ ,~ P-D-glucose,' m a l t ~ s e , cyclodextrin,8-'0 ~ and (1 + 3)- and (1 6)-linked mannose disaccharides'' have been reported, and have illustrated that carbohydrate dynamical behavior is both varied and sufficiently diverse to warrant further investigation. Due to the insight that dynamics simulations can provide concerning molecular flexibility and its role in conformational preferences and transitions, it is desirable that all of the commonly occurring disaccharides be systematically examined by these techniques to provide basic knowledge concerning the nature of glycosidic linkages. Among the common disaccharides, sucrose is of particular interest both because of its commercial importance and because it combines both a pyranoid and a furanoid ring. Sucrose apparently has only one low-lying primary glycosidic angle conformation on its vacuum energy surface,12 and does not appear from nmr studies to be oscillating between multiple structures in aqueous s ~ l u t i o n , l ~ - ' ~ although Christofides and Davies" have detected a competitive equilibrium between two forms in

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TRAN AND BRADY

dimethylsulfoxide (DMSO) solution. The crystal structure of this molecule is well known from diffraction studies,".18 and this crystal conformation has been found to be essentially the lowest energy structure in vacuum in conformational energy calculations. However, there has been some debate about the dynamical structure of this molecule in aqueous s ~ l u t i o n . ' ~ 19-21 - ' ~ ~ Furthermore, the ease of pseudo-rotation in furanoid rings has also been a matter of some interest,22 with Levitt and W a r ~ h e predicting l~~ very small barriers to interconversion in the ribose units of nucleic acids. Simulations of the vacuum dynamics of sucrose are reported here in an attempt to describe the types of conformational fluctuations that might be expected for this molecule, and to investigate the dynamical consequences of differing ring flexibilities when paired in a mixed disaccharide such as this.

METHODS In the calculations reported here, the equations of motion for each atom of the sucrose molecule were numerically integrated using the general molecular mechanics program CHARMM24and the potential energy function25 used in the preparation of the adiabatic conformational energy map reported in the accompanying paper.12 A Verlet integration algorithmz6 was used with a time step of l X s. All internal parameters were allowed to vary. Ensembles of trajectories were initiated by a random assignment of velocity components selected from a thermal distribution a t 300 K, and the initial coordinates were those for the minimum energy geometries identified in the adiabatic mapping of the sucrose conformational space. The trajectories were thermalized by gradual heating to 300 K and then further equilibrated to relax any artificial conditions arising from the initial condition selection. During the thermalization period, the temperature was regularly increased by 15 K increments a t 0.25 ps intervals until the desired value of 300 K was obtained. The trajectories were then equilibrated a t this temperature with periodic scalings of the atomic velocities if the average molecular temperature differed from the desired 300 K by more than -t5 K. For most of the trajectories, the duration of this heating/equlibration period was 20 ps but was extended by 10 ps in a few difficult cases of equilibration, especially for the highest local minima. The final 20 ps of each

trajectory was performed for data collection without further intervention. During this data collection period, the energy of the trajectories was well conserved, with no drift in the system temperature observed. Because static energy calculations found four other low-energy local minima in addition to the global minimum (labeled Sl-S5; see preceding paper), five different ensembles of trajectories were simulated. For the lowest energy conformation, an ensemble of twelve separate trajectories was calculated for more reliable statistical convergence than might be expected from a single trajectory 12 times longer in duration. For each of the four other local minima, ensembles of six trajectories were calculated. The total simulation time of all trajectories combined was 720 ps. In each ensemble, two trajectories were started from conformations with the GG form for the primary hydroxyl group of the glucose residue, corresponding to the crystallographic arrangement. In most of these cases, transitions from the GG to TG forms for this hydroxyl group were observed, either during the thermalization period or during the following data collection period. These transitions were observed early in the adiabatic mapping studies reported in the preceding paper,12 and led to the discovery that for all five minima, conformations of the TG type had the lowest potential energies. Thus for all the other simulations, the starting conformations had the TG conformation for this exocyclic group of the six-membered ring.

RESULTS Table I lists the mean values for the potential energies, the temperatures, and selected important internal coordinates (including the hydrogen-bond distances identified in the adiabatic mapping) for each ensemble. The values for energies and temperatures correspond to the average of the mean values of each trajectory of the ensemble during the entire measurement period. However, for the internal parameters, the values correspond only to the periods during which the most probable conformation occurred. Thus, some long-lived metastable conformers (duration > 1 ps) populated by transitions but that do not correspond to these most stable states were discarded from the statistics in order to define the most stable conformations. This procedure was also used to calculate the rms fluctuations, given in parentheses in Table I. The transitions observed during the simulation periods are discussed in detail below.

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

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Table I

s1 Potential Energy Temperature $JH

lco 0 x2g x3g x4g w6g x6g wlf Xlf

x 3f x 4f o 6f

X 6f

0 kcal/mol 301.0' K 3.2 - 52.6

117.3 - 46.9 - 38.6

43.6 175.5 30.4 - 179.7 42.0 39.9 62.3 - 63.8 49.7

d[01 . . . H'6fI d[05g . . . H'lf] d[05g . . H'6fI 2.09 A d[H'2g . . . 05f] d[02g . . . H'lf] d[H'2g . . . Olf] 2.02 A d[02g . . . H'6fI d[ H'2g . . 06f] d[02g . . . H'3fI d[ H'2g . . . 03f]

(10.5) (7.3) (2.9) (15.5) (16.0) (14.3) (13.1) (22.0) (7.2) (16.9) (16.3) (20.3) (10.6) (16.3)

s2 0.7 kcal/mol 300.1" K - 4.4 - 55.4

117.6 - 165.2

169.2 - 161.6

174.1 - 121.4 177.5 - 69.7 - 31.3 56.8 - 58.5 40.0

(11.6) (8.6) (2.9) (16.7) (14.0) (16.6) (13.9) (42.0) (9.0) (16.5) (21.7) (15.7) (10.7) (15.2)

s3 2.8 kcal/mol 301.6" K - 18.7 - 166.1

119.0 - 161.7

170.6 - 159.0

177.3 - 147.3 - 156.1 17.2 61.4 57.1 - 59.8 36.5 2.17 A

(0.18)

2.10 A

(0.17)

2.06 A

(0.20)

(11.1) (9.3) (2.8) (13.7) (14.0) (20.7) (14.0) (50.8) (9.4) (20.2) (14.0) (18.3) (12.7) (15.7) (0.26)

s4 3.6 kcal/mol 301.3" K - 35.3 - 179.7

119.9 - 30.7 - 43.0

41.3 171.1 36.5 - 163.0 - 112.0 - 62.7 59.7 - 56.7 42.5 2.14 A 2.58 A

(14.6) (14.5) (2.9) (30.0) (15.1) (14.6) (11.9) (18.8) (9.1) (44.0) (14.9) (17.9) (11.0) (15.2)

s5 3.1 kcal/mol 297.0" K 13.5 51.5 118.1 - 35.0 - 40.2

44.8 171.8 36.5 - 172.6 - 40.5 - 1.8 60.0 - 57.0 79.0

(9.9) (8.6) (2.9) (14.2) (14.9) (14.0) (10.9) (18.0) (11.6) (26.8) (27.8) (18.7) (11.6) (27.0)

(0.25) (0.77) 2.08 A (0.21)

(0.17)

The ensemble averaged relative potential energies listed in Table I for each conformer are in excellent accord with the adiabatic mapping calculations of the conformational energies.12 The energy difference between the S1 and S2 conformations is small (0.7 kcal/mol, compared to 1.0 kcal/mol in the static adiabatic mapping) and the lowest energy S1 form remains the global minimum. The three other stable conformations have comparable potential energies and the differences with the global minimum (about 3 kcal/mol) are approximately those found in the static adiabatic calculations. The ensemble-averaged internal coordinates obtained from the dynamics simulations are also close to the static values calculated from the various local minimum energy conformations (Table I, preceding paper). This agreement is particularly close in the case of the glycosidic dihedral angles ip and 1,5 in the S1, S2, S3 and S5 forms, where the mean differences are 2.4' and 3.6" respectively, which indicates that in this two-dimensional conformational space, the trajectories sample a surface centered on the minima. For the S4 conformation there is an interesting shift toward

2.22 A (0.40) 2.01 A

2.91 A

(0.85)

3.05 A

(0.91)

(0.18)

the S3 region. In all of the simulations, the trajectories stayed primarily within the 6 kcal/mol contour of the partial static maps with rare excursions out of these regions and with all completely contained within the 8 kcal/mol contour. For the dihedrals specifying the orientations of the hydroxyl groups, the dynamical ensemble-averaged values are consistent with the static structures with only a few exceptions. For those cases where this congruence does not hold, the large rms fluctuations are indicative of transitions resulting in oscillations between two or three metastable forms (including the local minimum), which makes it difficult (and problematic) to define the most stable geometry. This situation is particularly true of some x dihedrals of the primary hydroxyl groups (for example, x6g for the S3 conformation) and is dependent on the hydrogen-bond pattern. (See Fig. 1 of the preceding paper for the definition of the angle descriptions.) Such transitions were not observed for the w dihedrals that have mean values close (mean deviation = 1.6") to the TG, TG, and GG geometries, respectively, for the hydroxymethyl groups involving the atoms C6p. Clf, and

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TRAN AND BRADY

C6f. The fluctuations in these torsional angles are small compared to those for other torsional coordinates. S1 Conformation

All of the trajectories in the ensemble of simulations starting a t the global minimum were quite similar in behavior, remaining centered around the minimum energy structure, and could be readily understood in terms of the adiabatic energy surface. A typical trajectory in this region is shown in Fig. 1, superimposed on the local partial S1 energy map. In this example, 9 = 3.5" (rms = 9.5") and 4 = -52.7" (rms = 6.5"), and the + and 4 excursions during the simulation are primarily contained within in the 2 kcal/mol contour. It is interesting to note the asymmetry in the fluctuations in @ and 4 , with the larger fluctuations in + carrying the molecule to higher energy regions of the adiabatic map while regions of much lower energy on the adiabatic map are not sampled by comparable fluctuations in 4. Considering this ensemble of trajectories as a whole, excursions out of the 4 kcal/mol contour were exceptional and very brief, and such fluctuations never occurred in the left most extension of the map, regardless of the small transitions discussed below. The mean deformations of the pyranose and furanose rings in these simulations can be described by the average values of their CremerPople pucker parameter^.^^ For the glucose residue, the important parameters describing the deformation of the ring are Q, the puckering amplitude of the mean ring plane (mean value Q = 0.55 rms

A;

0.0

f3-

3 \ \ -

-60.0

-120.0 -100.0

-60.0

-20.0

20.0

60.0

! 100.0

Figure 1. History of a typical S1 trajectory for sucrose in (+, #) space, superimposed upon the S1 partial energy map. Contour intervals are at 2, 4, 6, and 8 kcal/mol above the local minimum, which is also the global minimum for the adiabatic surface.

= O.O4A), and 8, which specifies the specific conformational form, such as boat or chair ( 8 = 8.3"; rms = 4.2"). These values indicate that the pyranoid rings are fluctuating around the stable 4C, form of the crystal structure (Q = 0.556 A, 8 = 5.2"). As in the other simulations, transitions toward boat or twist-boat forms ( 8 = go"), or even toward half-boat or half-chair forms (8 = 45"), were not observed. For this reason, the pseudo-rotation parameter G2 is not included in these discussions, as it has little meaning near the poles of the spherical polar representation of the molecular puckering defined by the coordinates (Q, 8, G ~ ) .For this ring, the rnis fluctuations (especially for the 8 parameter) are not negligible, which indicates that the ring participates in the conformational relaxation phenomenon to lower the potential energy of some local interactions. The dynamical fluctuations of the furanoid ring are more pronounced, with the pucker parameter q2, related to the distortion from the mean plane, having a mean value of 0.35 i, (rms fluctuation = 0.07 A) and G2, specifying thv pseudo-rotation phase, having a mean value of 253.9" (3E form, rms fluctuation = 14.8"). The range of maximum and minimum observed values of G2, from around 220" to 300", covers all of the conformations from 'T3 to lT, iT $ $ :T *4E SZT, which are believed to interconvert readily without any eclipsing 1, 2 interactions.28 No transitions along the pseudo-rotation cycle from this group of low-energy conformations to the opposite set, iT P 3 E *:T S 4E @iT, were observed in any of these 12 S1 simulations, indicating barriers larger than those proposed by Levitt and W a r ~ h e for l ~ ~ribose. Clearly, however, the ring is not rigid even in the absence of a pseudo-rotation transition from one form to another. Of the twelve simulations, ten were performed with a starting TG conformation for the hydroxymethyl group of the glucose residue (06g = 180") and this geometry was kept during the thermalization period. Another simulation was initiated with the glucose exocyclic group in the GG form, but during the equilibration period, this group adopted the TG form. It would appear that the TG form is the most stable arrangement for this molecule in vacuum both because of these spontaneous transitions away from the GG starting form and since no long-lived transitions to the other two forms were observed. However, during the total simulation period of these 11 trajectories (220 ps), five brief transitions toward the GG form (w6g = - 60") were observed, followed by a return to the initial conformation after less than 1 ps,

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

group was started in the GG form and remained in this geometry throughout the equilibration period. However, a transition to the GT (w6g = +60") occurred approximately 1 ps into the data collection period, illustrated in Fig. 2a. As can be seen in Fig. 2(b and c), this transition induced persistent oscillations of the x6g dihedral between - 60" and 60", and the formation of a typical H'6g.. .06f hydrogen bond (mean distance = 2.08 A; rms = 0.21°), which was never observed with the TG conformation (mean distance = 5.2 A). The oscillations of the x6g dihedral might seem incompatible with the relative stability of this hydrogen bond, but there was an inverse correlation between the

demonstrating that the observed stability of the TG form with the potential energy function was not simply a failure to acquire sufficient energy to cross the intervening barrier. These transitions were correlated with the transition of x6g from +60" (the normal state when 06g = M O O , TG) to -60" (when 06g = -60", GG). It seems that this GG conformation of the primary hydroxyl group is dynamically accessible, but in the absence of a specific stabilizing factor, as for example, a hydrogen bond in vacuum, which could play a role equivalent to a lattice constraint in the crystal state, this form is not stable. The final trajectory of this ensemble was one in which the glucose exocyclic

120.0

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ti

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I

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981

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(b)

Figure 2. (a) History of the w6g torsion angle defining the glucose hydroxymethyl position for an S1 trajectory initiated with the GG conformation ( - SO'), exhibiting a transition to GT (tSO'). (b) History of the torsion angle x6g for this same trajectory. (c) History of the H'6g.. .06f hydrogen-bond distance for this same trajectory.

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TRAN AND BRADY

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5.0

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!l a 3.0 e m

i

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Figure 2. (Continued from the previous page.)

w6g and x6g fluctuations (cross correlation = -0.85 while in the GT form) caused by the presence of the hydrogen bond which allows the short hydrogen-bond distance between H'6g and 06f to be maintained. This phenomenon can explain the greater stability of the GT form, compared to the GG one, by the addition of one hydrogen bond. In the fructose residue, the hydroxymethyl group containing the atom Clf adopts the TG conformation (wlf = - 179.7') in all the simulations, with the lowest observed rms fluctuation (7.2') for any

of the torsion angles, since this conformation is stabilized by the most important intramolecular hydrogen bond, H'2g.. .Olf ( d = 2.02 A; rms = 0.17'), identified in the static adiabatic mapping. In this conformation, the X l f torsion angle is also stable (mean value = 42.0') with somewhat larger fluctuations (nns fluctuation = 16.9"), although normal for this type of dihedral. During the twelve simulations, only two brief transitions in this dihedral toward 180' (duration < 0.5 ps) were observed. For the other primary hydroxyl group, in-

5.0

2.0

I

I

4.0

I

8.0

!2.0

16.0

Time ( p s )

Figure 3. History of the interatomic distance 0 5 g . . .H'6f for an S1 trajectory in which the fructose primary hydroxyl group containing the C6f atom was in the GT conformation, illustrating that this orientation leads to the disruption of the normal hydrogen between these two atoms.

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

volving the atom C6f, the conformation is of the GG type (w6f = -63.8", rms = 10.6", and x6f = 49.7", rms = 16.3"). The stability of this arrangement can also be explained by the presence of the hydrogen bond 05g.. .H'6f, as found in static calculations. However, in one of the twelve simulations, the thermalization period led to a GT form (w6f = 59.9", rms = 13.0"; and x6f = - 53.6"; rms = 15.7"), which persisted throughout the entire 20 ps data collection period. As can be seen from Fig. 3, this conformation requires the disruption of the 0 5 g . . . H'6f hydrogen bond ( d = 3.77 A; rms = 0.66 A). As the potential energy of this simulation is 2 kcal/mol higher than the others and as the other parts of the molecule have a standard behavior, this local conformation might be considered unstable, with the energy difference due to the loss of the hydrogen bond. The other dihedrals (listed in column 1 of Table I), describing the positions of the secondary hydroxyl groups, have mean values consistent with the static calculations and all of the fluctuations are of comparable magnitudes. In the pyranoid ring, the 0 - H vectors have the "counterclockwise" orientation (see the discussion in the preceding paper for an explanation of this terminology). No transitions of these hydroxylbond vectors toward a "clockwise" direction were observed in any of the trajectories in this well. Also, the oscillations of x2g from approximately -60" to +60", with brief disruptions (duration < 0.5 ps) of the H'2g.. .Olf hydrogen bond, had no effect upon the x3g dihedral angle, which remained stable. S2 Simulations

Five of the trajectories in this ensemble of six simulations remained well within the 2 kcal/mol energy contour of the S2 well. These five trajectories, which constituted the data base for the S2 ensemble averaging, will be discussed together, and the sixth trajectory will be described separately below. As is the case for the other ensembles, Table I contains the average structural features of this set o f S2 trajectories. For these five simulations, the mean values of + and 1c/ were -4.4" and -55.4', respectively, which are quite close to the values characteristic of the S2 local minimum energy geometry. This is consistent with the approximately symmetric location of this minimum at the center of the 2 kcal/mol contour of the corresponding local energy map. For these trajectories, the mean values for the pucker parameters are Q = 0.55 A (rms fluctuation = 0.04 A) and 6' = 8.3" (rms

983

fluctuation = 4.3") for the glucose residue and q2 = 0.35 A (rms fluctuation = 0.06 A) and +2 = 259.8" (rms fluctuation = 12.3") for the fructose residue. These values and their fluctuations are very close to those of the S1 simulations, indicating similar behavior with respect to the deformation of the rings in these simulations. For the w6g dihedral, two trajectories were initiated with the GG conformation, but after the thermalization period, these torsion angles were found to be in the TG conformation as in the previous S1 simulations. This form is the most probable during the entire 120 ps of simulation time of all six trajectories (o6g = 174.1"; rms = 13.9"), but three brief transitions (of durations ranging from 0.5 to 2 ps) to the GG form were observed. Unlike the S1 simulations, even when the w6g dihedral was in its most stable form, the x6g dihedral continuously oscillated between + 180" and - 60" (see Figure 4), resulting in a "virtual" intermediate mean value of - 121.4" and a large rms fluctuation of 42.0. In such a case, it is difficult to define the most stable value for this dihedral in vacuum because of its rather free movement between the two forms. During the three periods when the 06g dihedral adopted the GG conformation, this x6g dihedral still oscillated, but between 180" and +60". These oscillations can be explained by the absence in vacuum of a hydrogen bond involving this hydroxyl group. For the hydroxymethyl group of the fructose residue containing the Clf atom, only the TG conformation was observed (olf = 177.5"; rms fluctuation = 9.0") and the X l f dihedral remained predominantly near -69.7" (rms fluctuation = 16.5") with only three brief transitions to +60" and one toward + 180". Figure 5a illustrates a trajectory in which two such transitions toward +60" occurred in X l f . This transition is correlated with the motions of the nearest secondary hydroxyl group of this residue, which underwent a transition of w3f from -60" to +60" and with the 02g ... H'lf hydrogen bond, which is broken during this transition [see Fig. 5(b)]. Only one transition of x2g, representing the motion of the other partner of this hydrogen bond [Fig. 5(c)], was observed, with x2g varying from 180" to -60". The other hydroxymethyl group of the fructose residue (containing the C6f atom) also is apparently in a relatively stable conformation in the GG geometry (w6f = -58.5"; rms = 10.7") since all five of these simulations exhibit this behavior during the data collection period and the last simulation, discussed below, initiated with this GG conformation, experienced only a brief transition to the GT form (dura-

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TRAN AND BRADY

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I

I

4.0

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I

300.0 240.0 X6g

180.0 120.0

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Figure 4. History of the x6g dihedral angle for a typical S2 trajectory corresponding to the T G conformation for the primary hydroxyl group of the glucose residue.

tion of 2 ps) before returning to the GG form for the remainder of the simulation. The stability of this GG form is also consistent with the static minimum energy conformer of the adiabatic energy surface, and the x6f dihedral adopts the only value (x6f = 40.0"; rms fluctuation = 15.2") that leads to the formation of the second important stabilizing hydrogen bond in this conformation, the 05g.. .H'6f hydrogen bond. In fact, the conformational stability of the two hydroxymethyl groups of the five-membered ring (especially X l f and x6f, compared to x6g) can be explained by the presence of these hydrogen bonds. As for the secondary hydroxyl groups, the orientations of the OH vectors are consistent with those observed for the corresponding S2 local minimum energy conformer, excepting the brief and isolated transitions away from these expected values. No reorientations of the clockwise direction of the OH bonds on the pyranoid ring, which might lead to S1-type conformations, were observed during any of the six simulations. The sixth trajectory of this S2 ensemble differed from the others in that it underwent an extended spontaneous excursion in 6 and Ic/ space into the " upper valley" in the left part of the local energy well [see Fig. 6(a)] during the last 6 ps of the data collection period. In terms of potential energy, this fluctuation is not particularly unusual, and the trajectory is almost completely contained within the 6 kcal/mol contour. However, this period corresponded to conformations of + significantly different from those near the S2 local minimum energy structure. While in this region of gly-

cosidic angle space, the deformation of the pyranose ring was slightly greater ( Q = 0.57 A, rms fluctuation = 0.04 A; and 0 = 9.7", rms fluctuation = 5.2") but the ring remained very close to the stable 4C, form. However, the furanose ring underwent important conformational changes. The pucker magnitude q2 remained near the previously observed values ( q 2 = 0.34 A; rms fluctuation = 0.08 A), but there was a significant shift in the pseudo-rotation phase G2 ( G ~= 212.4"; rms = 74.9"), as the furanoid ring underwent a conformational transition between two separate states [see Fig. 6(b)]. As long as the trajectory stayed near the local S2 minimum in (G, 4) space (from 0 to 14 ps of the data collection period), the mean value of G2 was approximately 250", with a range from about 230" to 300", which covers all of the conformations from iT to lT (cf. Fig. 13, preceding paper), as in the other trajectories. However, during the last 6 ps of the trajectory (during the frequent excursions in the left part of the local energy well), the mean value of this parameter was near 90" with frequent oscillations from 60" to 120". This range in G2 includes all of the conformations between iT and 5 *T, the other family of easily interconverting conformers corresponding to the opposite pucker of the ring. Unlike the ribose case,29 this transition occurs through ,E (G2 = 180"), which corresponds to the western part of the five-atom-ring conformational wheel (cf. Fig. 13, preceding paper). I t is interesting to note that this transition was preceded by other unsuccessful "attempts" ( G2 = 200"). This trajectory would indicate that while the furanose ring does not undergo free rotation

DISACCHARIDE CONFORMATIONAL FI,EXIBII,ITY. I1

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Figure 5. (a) History of the dihedral angle X l f for an S2 trajectory in which this dihedral angle specifying the orientation of the fructose hydroxymethyl group containing the Clf atom underwent two brief transitions from the TG conformation toward the GG. (b) History of the interatomic distance for the 0 2 g . . .H'lf hydrogen bond calculated from this same trajectory. (c) History of the x2g torsion angle calculated from the same trajectory.

between the two primary groups of conformers, it is more flexible with this potential energy function than the pyranoid ring, which was not observed to undergo any spontaneous conformational changes. Similar infrequent pseudo-rotational transitions for five-membered carbohydrate rings have been observed in molecular dynamics simulations of nucleic 31 The internal deformation of the five-membered ring during the last 6 ps had important consequences for the orientation of the 0 - M vectors of

the fructose residue. For example, the x4f dihedral no longer had the mean value found in the other simulations (about 60") and oscillated between + 60°, - 60°, and 180". I t is perhaps mare interesting to look a t the 0-H bonds involved in hydrogen bonds in the S2 conformation or expected in the new conformations in the left part of the energy well. For the X l f dihedral, there was no significant correlation with the pseudo-rotation phase variations. Since the interring hydrogen bond 0 2 g . . . H'lf is not physically possible in the left part of the S2

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Figure 5. (Continued from the previous page.)

region (see Fig. 5 of the preceding paper), this linkage was broken and X l f no longer needed to undergo dramatic changes in order to maintain this stabilizing factor. From Fig. 6(c), which illustrates the variations of the 02g ... H'lf distance, it is clear that this hydrogen bond is not retained and that the observed fluctuations in the last 6 ps are due to the fact that the trajectory does not remain permanently in the left part of the map but occasionally returns to the region around the local minimum energy position. The x6f dihedral is affected more by the variations of the pseudo-rotation phase, not only because of the breaking of the 05g.. . H'6f hydrogen bond, which is not possible in the left region, but also due to attempts to create the H'6g.. .06f hydrogen bond which is predicted for this region from the adiabatic energy mapping. Figure 6(d and e) illustrates these two 0 . .. H distances (05g.. .H'6f and H'6g.. .06f respectively). The observed fluctuations in both cases can be explained by the oscillation of the trajectory between the left part of the map and the local S2 minimum since this left region does not correspond to a local minimum that could lead to a more stationary trajectory. S3 Simulations The ensemble of six trajectories that were begun in the S3 well divided naturally into two categories. The first of these categories included three trajectories contained within the inner energy contours of the well. In these simulations, the 4 kcal/mol contour circumscribed more than 95% of the trajectory time and the 6 kcal/mol line was never

reached. The second category includes the other three simulations where the molecules remained primarily near the local minimum, but underwent a t least one excursion out of the 6 kcal/mol contour to the left and top part of the partial map toward the S2 region, with one of the simulations undergoing a spontaneous transition to the S2 region (discussed below). Although the trajectories of the two other simulations in this second category returned to the region near the S3 minimum, these cases were discarded from the ensemble averaging for this well in order to define the quasi-stable primary behavior of the S3-type conformation. Thus column 3 of Table I lists the mean values and fluctuations of the important internal parameters of the first category only. The average values of C#I and I/I for this subensemble are quite close to the static values calculated from the local S3 minimum, and the fluctuations are similar to those of the S1 and S2 simulations. The pucker parameters for these three compact trajectories are Q = 0.57 A (rms fluctuation = 0.04 A) and B = 9.2" (rms fluctuation = 5.1O) for the glucose residues, and qz = 0.39 A (rms fluctuation = 0.05 A) and (pz = 247.8' (rms fluctuation = 12.8") for the fructose ring. In these three simulations the hydroxymethyl group of the glucose residue always existed in the TG conformation (w6g = 173.3'; rms fluctuation = 14.0"). This form is apparently the most stable and even when the simulations were initiated in the GG form, this group rotated to the TG orientation during the thermalization period. During the six simulations, only one short transition (duration < 0.5 ps) was observed toward -60" (the GG form) for this w6g

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

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Figure 6. (a) History of an S2 trajectory for sucrose in (@, 4 ) space, superimposed upon the S2 partial energy map, for a trajectory that underwent a confonnational fluctuation into the “upper valley” in the left part of the map. Contour intervals are at 2, 4, 6, and 8 kcal/mol. (b) History of the Cremer-Pople pucker parameter I#I~ for the fructose from this same trajectory, indicating a change in pseudo-rotation phase. (c) History of the 02g.. . H’lf hydrogen-bond interatomic distance during this trajectory. (d) History of the 05g. . . H’6f and (e) H’6g.. .06f hydrogen-bond interatomic distances from this trajectory.

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Figure 6. (Continued from the previous page.)

dihedral, followed by a return to the mean position. In contrast, the x6g dihedral was found to be very mobile (for the trajectories in both categories), which explains the very high value of the corresponding rms fluctuation (50.8"). Figure 7 illustrates typical variations for this torsion angle where the values near 180" seem preferred (as in the static local minimum) but the two other values (near +60° and -60") are also possible, with frequent transitions between these values. As discussed for the S2 simulations, the lack of a hydrogen bond localizing the H'6g atom could explain the free rotation of the corresponding 0-H vector in vacuum.

The two hydroxymethyl groups of the fivemembered ring have stable conformations with rather low fluctuations (see Table I), particularly for the group containing the H'6f atom, which is involved in a presumably weak hydrogen bond ( 0 1 . . .H'6f). For the olf, o6f, and x6f dihedrals, no significant deviations from their mean values were observed, and for X l f , there were only two very brief fluctuations toward k 120". For the secondary hydroxyl groups of this S3 type, x2g and x3f have the lowest fluctuations (13.7" and 14.0", respectively), since they participate in the other interring hydrogen bond found in the static adiabatic energy mapping of this S3 region

DISACCHARIDE CONFOHMATIONAI, FLEXIBILITY. I1

( 0 2 g . . . H'3f). The orientations of all of these 0 - H groups are stable and the clockwise arrangement of those of the glucose residue is maintained throughout without even transient attempts a t reorientation. The third possible hydrogen bond identified for this well from the partial S3 energy mapping (see Fig. 8 of the previous paper), 0 5 g . . .H'lf, was not found in these simulations ( d = 3.8 A; rms fluctuation = 0.3 A) since its formation requires fluctuations outside of the surface sampled by these trai ectories.

cose hydroxyl groups). During the transition, no change in this orientation of the glucose hydroxyl orientations occurred; t h a t is, the system did not relax t o the adiabatic map. However, the observed trajectory is quite consistent with this combined energy surface. T h e occurrence of such transitions in trajectories of sufficient length is to be expected since the S2 well is lower in energy (there is a mean potential energy difference of 2.1 kcal/mol between the two wells, averaged over all of the trajectories in each). The trajectory remained within the 6 kcal/mol contour throughout its history, and its path followed the lowest energy route between the two regions over most of its course. Figure 8(b) displays the history of the # angle alone for this transition. While deformations of the furanoid ring may have played a minor role in this conformational transition, the six-membered ring was not significantly affected, with the mean values of its pucker parameters and their fluctuations being comparable t o those found in other simulations ( Q = 0.51 A, rms fluctuation = 0.04 A; and 6' = 9.0", rms fluctuation = 4.7"). The initial and final molecular structures thus have the pyranoid ring in the 4C, form and significant departures from this conformation were not observed during the transition. For the five-membered ring, the fluctuations of the pucker parameters were only slightly higher than in the other simulations ( q 2 = 0.41 A, rms = 0.05"; and G2 = 261.6"; rms = 14.5"). Figure 8(c) depicts the variations of this pseudo-rotation phase. The extreme values of r$2 observed during this simulation, from around 220" to 300", are sampling the same family of conformations seen in the other

S 3 4 2 Transition

Only one transition from one local energy well in (+, # ) conformation space to another was observed in all of the simulations reported here. This transition, illustrated in Fig. 8(a), began in the S3 well and ended in the S2 one. As mentioned above, in two other simulations initiated in the S3 minimum, unsuccessful attempts a t transition were observed, and in one of these, the trajectory reached the minimdm energy region of the S2 map ( = - 60", - 80" ) but subsequently returned to the S3 local minimum. Since the starting conformation is of the S3 type and the final one is of the S2 type, this trajectory is superimposed on a synthesis of the S3 and S:! partial maps, rather than the local region of the adiabatic energy map; the energy contours thus differ slightly from those of the adiabatic map. This map was used since during this trajectory the molecule is essentially either in an S2 or S3 conformation, while many of the points in the adiabatic niap of this region are from the S1 partial map (with an opposite orientation of the gik-

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Figure 7. History of the x6g torsion angle for a typical S3 simulation of sucrose.

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Figure 8. (a) History of an S3 trajectory in (@, I)) space that underwent a transition to the S2 well, superimposed upon a synthesis of the S2 and S3 maps. Contour intervals are at 2, 4, 6, and 8 kcal/mol. (b) History of the angle I) alone for this transition. (c) History of the Cremer-Pople pucker parameter +2 for the fructose ring during this transition. (d) History of the x3f torsion angle during this transition. (e) History of the X l f torsion angle during this transition.

normal trajectories ( 'T3 to 4T5) with no transition to the other form as was observed in the anomalous S2 trajectory. The conformational transition of this trajectory was accompanied by changes in the orientations of several 0 - H bond vectors, particularly those involved in hydrogen bonds in either the S3 or S2 forms. Figure 8(d) depicts the variation of the x3f dihedral torsion during this transition from around + 60" (before the transition) to approximately

- 60" after the transition, which was accompanied by a change in the mean 02g ...H'3f hydrogen bond distance from 2.0 in the S3 form before the transition to a mean value of 4.1 A in the S2 conformation, where this hydrogen bond is broken. A t the same time, the X l f dihedral underwent a transition from a value of approximately 10" before the transition to approximately -60" in the S2 conformer after the transition [Fig. 8(e)]as the characteristic interring 02g. . .H'lf hydrogen bond

A

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

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Figure 8. (Continued from theprevwuspage.)

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of the S2 conformation is formed by exchange. Before the transition the mean distance between these two atoms was 4.3 A, and this mean distance was 2.1 A after the transition. As a result of this hydrogen-bond exchange, there was always one 0 - H vector of the fructose residue pointed toward the pyranose ring, and as one interring hydrogen bond broke, the other almost immediately replaced it, reducing the energetic cost of the conformational fluctuation. In the transition only the fructose hydroxyl groups reoriented to effect this hydrogen-bond exchange; the orientation of the C2 hydroxyl of the glucose ring was unchanged; before the transition the mean value of the x2gd dihedral angle was 161.7' (rms fluctuation = 13.7'), and after the transition the mean value of this angle was - 165.2' (rms fluctuation = 14.7'). The transition thus required no change in the basic clockwise orientation of the glucose hydroxyl bond vectors, which would have required a larger activation energy as several hydrogen bonds were simultaneously broken, carrying the system over to the S1 surface. It should be noted that Christofides and Davies" have suggested that for sucrose in DMSO solution a competitive equilibrium exists between two different conformations. Under these conditions, there are no possible hydrogen donors for exchanges of hydrogen bonds with the solvent, which may be somewhat more like vacuum conditions than is aqueous solution. One of these conformations may be approximately the present S2 form since it has the 0 2 g . . .H'lf hydrogen bond, while the other conformation may correspond to the S3 form, with the 02g.. .H'3f hydrogen bond. Thus the S3-S2 transition found in the present calculations is consistent with their hypothesis. Furthermore, from their experimental nmr measurements (magnitudes of isotope shifts), they have deduced that the equilibrium favors the conformation containing the 0 2 g . . .H'lf hydrogen bond (S2 form), and this result is in good agreement with the relative energy difference between the S2 and S3 conformations. S4 Simulations

An ensemble of six trajectories was initiated from the S4 minimum energy conformation, and the mean structural features of this simulation are also summarized in Table I. This ensemble exhibited the largest shifts in + and Ic/ from the values of the corresponding local minimum energy structure of any of the ensembles, with larger fluctuations. These larger deviations result from the fact that

while the 4 kcal/mol contour for this local map is well centered around the local minimum energy position, the relaxation resulted in a nonisomorphic enlargement of the allowed region such that the 6 kcal/mol is not symmetric about this point. The molecules remained in the S4 geometry throughout the simulations, with no tendency toward the opposite hydroxyl arrangement of the S3 surface. In one simulation, two excursions out of the 6 kcal/mol contour occurred toward the upper left region of the local map, such as occurred in the transitions from S3 to S2. If this fluctuation, which appears to have actually gone somewhat past the crest of the intervening barrier, had continued on over to the adjacent energy well, the molecule would have been in the S1 form of the global minimum energy well. The mean values for the pucker parameters for the glucose rings in these simulations were similar to those observed in the other simulations ( Q = 0.57 A, rms fluctuation = 0.03 A; and 0 = 8.9", rms fluctuation = 4.5'); for the fructose ring, g , = 0.41 A (rms fluctuation = 0.06') and ,$t = 245.0' (rms fluctuation = 11.3"), quite close to the values observed for the stable S3 trajectories. As was the case for the other ensembles, two trajectories were performed with a GG starting conformation for the hydroxymethyl group of the pyranose ring, but in both cases this group underwent transitions away from this form during the thermalization period. The TG orientation was again found to be the most probable, as in the other simulations, with the w6g dihedral for the most part remaining near 180" (u6g = 171.1", rms fluctuation = 11.9'). The x6g dihedral was also stable (x6g = 36.5", rms fluctuation = 18.8') except when this primary hydroxyl group was in the GT form, where all three orientations, + 60', - 60", and B O O , were observed for this torsion. The orientations of the primary hydroxyl groups of the furanose ring (TG for w l f and GG for w6f) were also quite stable in these trajectories with small fluctuations. This stability also applied for the 06f-H'6f bond involved in a hydrogen bond (x6f = 42.5"; rms = 15.2'), but it was impossible to define the stable orientation for Olf-H'lf since the dihedral X l f continuously oscillated between +180' and -6O", which explains the mean interatomic distance value and the large fluctuation reported in Table I. Table I also lists the torsional orientations x2g, x3g, and x4g of the secondary hydroxyl groups of the glucose residue, and these dihedrals, with their counterclockwise orientations, have mean values similar to those found in the S1 simulations. No

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

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Figure 9. (a) History of the torsion angle x2g in a typical S4 trajectory. (b) History of t h e H 2 g . . .03f hydrogen-bond distance during the same trajectory. (c) History of the H'2g.. .06f hydrogen-bond distance for t h e same trajectory.

significant disruptions or fluctuations away from t h s pattern that might lead to the S3 form were observed. although the x 2 g dihedral did undergo large fluctuations. Figure 9(a) illustrates a typical history of this dihedral in these trajectories. The variation from -60" to +60° does not correspond to an attempt at reorientation (the magnitude of these transitions is not sufficient) but is the result of the competition between the two possible hydrogen bonds (H'2g. . .03f and H'2g.. .06f) in which this atom can participate in the S4 form. Figure 9(b and c) illustrates the histories of these hydrogen-bond distances for the same trajectory, from

which it is clear that both hydrogen bonds cannot exist simultaneously, as found in the static energy mapping of this S4 well (see Fig. 9 of the preceding paper). When x2g is near -6O", the H'2g ...06f hydrogen bond may occur (depending on the values of $I and +), and when x2g is near +60", the other hydrogen bond is possible. The continual oscillation between these two forms results in the large mean values for these hydrogen-bond distances in Table I. Similarly, the weak hydrogen bond 0 5 g . . . H'lf, which is not possible for all values of @ and \c/ in this well, has a large mean value due to occasional disruptions of the bond.

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Figure 9. (Continued from the previous page.)

S5 Simulations A final ensemble of six trajectories was performed for starting coordinates in the S5 minimum energy conformation. All of these trajectories remained well localized in the vicinity of the local minimum with low rms fluctuations in C$ and 4 (Table I, column 5). This stability is not surprising in view of the isolation of the S5 energy well in glycosidic angle space, with a restricted allowed region separated from the global minimum energy region by high barriers. The secondary hydroxyl groups in these trajectories, which are in the counterclockwise arrangement on the glucose group, are stable to disrupting fluctuations; however, in this higher energy local minimum energy well, the exocyclic hydroxymethyl groups appear to be more mobile than in the lower energy regions of glycosidic torsion angle space. As with the other ensembles, four of the trajectories were initiated with the glucose hydroxymethyl group in the TG orientation, and two trajectories began with this group in the GG arrangement. In most of the simulations, including one of the latter cases, the TG orientation was the observed stable form during the data collection period, but in one of the latter simulations, this group spent significant periods in all three wells. When 06g was in the GG form ( - 60°), x6g was rather stable near +60", but when 06g was in the TG orientation ( - 180"), x6g had two favored values ( +60° and -6O"), and when 06g was in the G T form ( - +60°), x6g oscillated between -60"

and 180". In one trajectory, a spontaneous transition occurred for the hydroxymethyl group of the fructose residue involving the Olf atom, from the apparently most stable TG conformation to the GG form (olf varying from 180" to - 60") without a significant increase of the mean potential energy. Spontaneous transitions for the other hydroxymethyl group of the fructose residue (involving the 06f atom) were observed in two trajectories, from the most probable GG form (06f - 60") to the TG orientation (06f 180"). Figure 10(a) illustrates one of these transitions, which induced an oscillation of the torsion angle x6f between its three low-energy states (+60", -60", 180") and the breaking of one of the system's stabilizing hydrogen bonds (02g.. . H'6f), as shown in Fig. 10(b). These conformational fluctuations appear to be characteristic of this higher energy local minimum.

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Conclusions

In the dynamics simulations reported here, sucrose in vacuum was found to be a relatively rigid molecule, as has previously been concluded from a variety of experimental measurements. This disaccharide, of course, is not completely rigid, as was suggested by previous molecular mechanics analyses, and like most biopolymers undergoes a rich variety of motions on an atomic scale. In the present simulations, however, ordinary conformational fluctuations were confined for the most part

DISACCHARIDE CONFORMATIONAL FLEXIBILITY. I1

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Figure 10. (a) History of the torsion angle 06f from an S5 trajectory that underwent a spontaneous transition from the GG to TG orientation. (b) History of the hydrogen-bond distance 02g.. .H’6f for this same transition.

to a restricted region around the crystallographic values of @I and 4. The adiabatic energy map of (@I, 4 ) space demonstrates that no alternative low-energy wells exist in vacuum, making large conformational fluctuations or transitions unlikely. (However, the primary minimum region A does consist of two related conformations that differ in the directionality of the hydrogen bond “rings” of the glucose moiety, l2 the S1 and S2 forms.) Transitions in the pyranoid ring conformation were not observed in these trajectories, and only one transition of the furanoid ring between the two major forms was observed, although within these two

conformational families transitions are occurring frequently between the various twist and envelope forms that make up each region. The infrequency of transitions in this ring indicates that the major furanoid pseudo-rotational barrier, not yet quantitated for this potential energy function, is not negligible and that pseudo-rotation for this ring is not “free.” Sucrose is thus found to have considerably less conformational freedom than typical dipeptides or disaccharides such as maltose. In general, the adiabatic energy map was found to be adequate to explain the majority of the observed motions for sucrose. However, the failure

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TRAN AND BRADY

of the clockwise hydrogen-bonding pattern of the glucose hydroxyl groups in the S2 and S3 simulations to relax to the counterclockwise pattern of the S1 global minimum energy structure, even during the S3-S2 transition, indicates that relaxation to the adiabatic surface is slow in vacuum compared to the time scales of conformational fluctuations. This slow relaxation is consistent with the results found for maltose in vacuum with this potential energy f ~ n c t i o n . ~ In part, the observed conformational stability for this molecule may be an artifact of the vacuum conditions with the present potential energy function, which employs the larger atomic partial charges appropriate for aqueous solutions. Simulations of glucose and maltose in vacuum using this potential have shown little tendency for ring hydroxyl groups to undergo transitions in orientation due to the formation of stable intramolecular circuits of hydrogen bonds in the absence of solvent hydrogen bond partners, while preliminary simulations of the aqueous solvation of a-n-glucopyranose3' have found that in the presence of water molecules such reorientations occur readily, although often at a slow rate due to frictional damping. As a result of such facile hydroxyl rotations, sucrose in solution would be readily able to relax to the adiabatic surface during conformational transitions. I t is not clear, however, how the presence of the water molecules might make the free energy surface in solution differ from the vacuum adiabatic potential energy surface. Recent nmr studies indicate that the intramolecular 02g ... Olf hydrogen bond observed in the crystal structure is maintained in aqueous s ~ l u t i o n , ' ~ - 'although ~ previous Raman and diffraction experiments suggested that this bond was lost in dilute aqueous s o l ~ t i o n . ' ~The - ~ ~present studies offer little indication of a pronounced tendency in vacuum for the intraring hydrogen bond to be broken. However, the observation of an S2 trajectory in which this hydrogen bond was spontaneously broken accompanied by pseudo-rotational changes in the furanoid ring is suggestive that such conformational changes might be possible in aqueous solution. Clearly an extensive solution simulation will be necessary to address this question properly. Given the flexibility of the two rings, and in particular the fructose ring, such a conformational shift could not be ruled out completely from the present studies. T h e authors thank S. Perez, L. Madsen, and S. Ha for helpful discussions. This work was supported in part by

NIH grant number GM34970 and by Hatch project NYC 143431, USDA, and by a travel grant t o V.T. from INRA.

REFERENCES 1. Brooks, C. L., Karplus, M. & Pettitt, B. M. (1988) Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, Advances in Chemical Physics, Vol. LXXI, Wiley, New York. 2. McCammon, . & Pople, J. A. (1975) J . Am. Chem. SOC. 97, 1354-1358. 28. Stoddart, J. F. (1971) Stereochemistry of Carbohydratt.s, Wiley, New York.

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29. Harvey, S. C. & Prabhakaran, M. (1986) J . Am. Chem. SOC.108, 6128-6136. 30. Harvey, S. C., Prabhakaran, M. & McCammon, J. A. (1985) Bwpolymers 24, 1169-1188. 31. Singh, U. C., Weiner, S. J. & Kollman, P. (1985) R o c . Natl. Acad. Sci. USA 82, 755-759. 32. Brady, J. W. (1989) J . Am. Chem. SOC. 111, 5155-5165.

Received October 3, 1988 Accepted March 22, 1989

Disaccharide conformational flexibility. II. Molecular dynamics simulations of sucrose.

Molecular dynamics simulations have been used to study the motions in vacuum of the disaccharide sucrose. Ensembles of trajectories were calculated fo...
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