Computer Modeling of Carbohydrate Molecules - American Chemical

Chapter 13

Downloaded by UNIV OF QUEENSLAND on January 31, 2016 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch013

Conformational Flexibility of Sucrose Static and Dynamical Modeling 1

2

V. H. Tran and J. W. Brady 1

Institut National de la Recherche Agronomique, B.P. 527, 44026, Nantes, France Department of Food Science, Cornell University, Ithaca, NY 14853-7201

2

In analyzing the conformational properties of carbohydrates, i t has often been the practice to consider individual monomer rings to be rigid units, with the only molecular flexibility lying i n torsional rotations about the linkage bonds. However, conformational energy maps prepared using this assumption can be quite misleading in deciding which conformations are energetically allowed, and almost useless in understanding the likely motions of disaccharides, such as might be computed in molecular dynamics simulations. Molecular f l e x i b i l i t y can be incorporated into conformational energy maps by preparing relaxed or adiabatic energy maps. However, a number of operational difficulties complicate the calculation of relaxed energy maps. This paper discusses some of these practical problems which arise in the preparation of relaxed conformational energy maps for complex dimers like disaccharides, and how these problems complicate the physical interpretation of such maps. The importance of molecular flexibility is illustrated through the application of flexible conformational energy mapping and molecular dynamics simulations to sucrose.

A particularly common application of computer modeling to carbohydrate molecules is the use of calculated conformational energy maps for disaccharide glycosidic linkages as a tool in understanding oligosaccharide conformational structures (1). Although past studies have often treated the internal degrees of 0097-6156/90/0430-O213$06.00A) © 1990 American Chemical Society

In Computer Modeling of Carbohydrate Molecules; French, Alfred D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


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freedom of disaccharides as r i g i d , except for the g l y c o s i d i c t o r s i o n angles themselves, i t i s now widely accepted that the r i n g forms of sugars are not completely r i g i d , and that the i n t e r n a l f l e x i b i l i t y of these rings can strongly couple with g l y c o s i d i c rotations to substantially a f f e c t calculated conformational energy maps (2-4). For this reason, i t can be worthwhile to calculate relaxed or adiabatic energy maps i n which the molecular structure i s relaxed by energy minimization at each point on the g l y c o s i d i c map i n order to r e l i e v e i n t e r n a l strains (5). I t i s also possible to use molecular dynamics simulations (6) to d i r e c t l y model the motions that a disaccharide molecule might undergo, and to r e l a t e these motions to the calculated conformational energy map. Recently, we performed such a series of calculations for the mixed disaccharide molecule sucrose using the general molecular mechanics program CHARMM (7). A complete description of t h i s work has been presented elsewhere (8,9), and we s h a l l describe here only the general strategy f o r such studies, using the sucrose work as an example. In p a r t i c u l a r , we w i l l focus on technical d i f f i c u l t i e s which arise i n these calculations, including possible nonphysical a r t i f a c t s , and examine the d i s t i n c t i o n between adiabatic and relaxed maps and their physical interpretation. Adiabatic and Relaxed Energy Maps Ramachandran-like conformational energy maps (1) represent disaccharide energies as depending only on two degrees of freedom, φ and φ, when actually there are a very large number of possible combinations of values f o r the many i n t e r n a l degrees of freedom on which the t o t a l energy depends, such as the various bond lengths and angles and the other i n t e r n a l t o r s i o n angles. F l e x i b l e monomer conformational energy maps are obtained when the molecular geometry i s relaxed by energy minimization at each value of φ and •φ on a regular grid. Any such conformational energy map i n which energy minimization has been used to r e l i e v e i n t e r n a l strains can be referred to as a "relaxed" energy map. However, because of the high dimensionality of the s t r u c t u r a l problem (due to the large number of bonds, angles, hydroxyl orientations, etc.) there w i l l i n general be a very large number of structures which are l o c a l minima for the empirical energy function. This s i t u a t i o n can be v i s u a l i z e d by noting that f o r any given value of φ and -φ there are many possible arrangements of a l l of the hydroxyl groups and primary alcohols i n the monomers. For any of these l o c a l minimumenergy structures, any small change i n geometry i n i t i a l l y produces an increase i n energy. However, only one of these structures w i l l have the lowest possible energy consistent with the s p e c i f i e d values of the glycosidic torsion angles. A conformational energy map i n which only these lowest energy values are p l o t t e d as a function of the glycosidic angles w i l l be referred to i n t h i s paper as an "adiabatic" energy map. The single lowest energy structure possible for the molecule, including allowing φ and -φ to vary, i s referred to as the global minimum energy structure. The d i f f i c u l t problem of finding these lowest energy structures i s often referred to as the "multiple-minimum" problem, which arises i n any minimization of a function of many variables, and which has



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contributed to f r u s t r a t i n g e f f o r t s to predict biopolymer structures from sequence using molecular modeling techniques (10). Calculating a meaningful relaxed energy map f o r a disaccharide molecule i s not necessarily straightforward due to the complications which arise from the multiple-minimum problem. No general mathematical solution to this problem e x i s t s . As a r e s u l t , energy minimization from any given s t a r t i n g structure f o r a given molecule w i l l i n general produce only the nearest l o c a l minimum-energy structure not separated from the s t a r t i n g point by any s i g n i f i c a n t b a r r i e r s . The conformation and i t s energy thus produced w i l l therefore depend strongly upon the s t a r t i n g structure. In practice, the results may also depend on the minimization algorithm. These d i f f i c u l t i e s imply that a relaxed map produced by simply rotating an a r b i t r a r y disaccharide structure about the glycosidic torsions to various values of φ and ψ, followed by minimization, may produce unusual and p h y s i c a l l y u n l i k e l y structures, even i f the rotations are done i n a systematic fashion. This d i f f i c u l t y arises because some of the s t a r t i n g structures i n such a regular procedure w i l l themselves almost c e r t a i n l y be p h y s i c a l l y u n l i k e l y . Overcoming t h i s problem would require performing minimizations for an extremely large number of s t a r t i n g structures at each value of φ and ψ to f i n d the conformation with the lowest possible energy. In most cases i t i s not p r a c t i c a l to make such a thorough search due to the l i m i t a t i o n s of available computer time. Furthermore, f o r reasons discussed below, an adiabatic map may i n some cases not be the most useful of the possible relaxed energy maps. The most p h y s i c a l l y meaningful map would be one i n which the relaxation by minimization occurred i n a manner as close as possible to the actual physical process being represented. I f one started from the global minimum-energy structure (assuming that i t i s possible to i d e n t i f y that structure at the beginning of the study!), then perturbing the conformation to values of φ and -φ that are close by i n configuration space should produce only small changes i n the other conformational variables, thus perhaps reducing the number of p o s s i b i l i t i e s that would have to be investigated by separate minimizations from d i f f e r e n t s t a r t i n g structures. As one moved further away from this minimum-energy structure however, the other i n t e r n a l degrees of freedom would presumably change by varying amounts, and at some point an a r b i t r a r y distance away i n the (φ,φ) map, some other combination of the various internal coordinates than that found i n the global minimum-energy structure may produce the lowest energy at that (Φ,Ψ) gridpoint when minimized. A map that ignored t h i s s h i f t and continued to p l o t the energies of those minimized structures which had f o r the most part the same general conformation f o r these other i n t e r n a l variables as the s t a r t i n g minimum, regardless of whether they were the absolute lowest values at the g r i d point, would then be a " l o c a l " relaxed surface, or " p a r t i a l " relaxed surface. Such a surface might represent the energy surface over which the molecule would move during a dynamical s t r u c t u r a l f l u c t u a t i o n i f there i s no relaxation to any possible lower energy forms.


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Calculation of Relaxed and Adiabatic Maps f o r Sucrose Very few calculations of adiabatic energy maps f o r disaccharides coupled with molecular dynamics simulations have been undertaken, p a r t i a l l y as a r e s u l t of the great expense and labor involved i n such studies. One molecule which has been studied by both of these types of molecular mechanics calculations i s sucrose. Sucrose was selected f o r study for several reasons. This molecule, which i s the dimer of a pyranoid glucose r i n g and a βfuranoid fructose ring, connected by an α[1-»·2] linkage, offers the p o s s i b i l i t y of studying the interplay of f l e x i b i l i t y between the furanoid r i n g and the more r i g i d six-membered r i n g . I t i s a p a r t i c u l a r l y good molecule f o r t h e o r e t i c a l modeling since i t has been extensively studied by a v a r i e t y of experimental techniques. The c r y s t a l structure of this molecule has been determined by both x-ray (11) and neutron d i f f r a c t i o n (12) analysis. Several NMR studies of the conformation of sucrose have been reported i n the l i t e r a t u r e f o r molecules i n both aqueous (13,14) and DMSO (15) solution. Mathlouthi et a l . (16) have studied sucrose using Raman spectroscopy, and some previous molecular mechanics work i s also available f o r comparison (13,12) . Preliminary investigation revealed that sucrose i s s i g n i f i c a n t l y r e s t r i c t e d i n i t s conformational fluctuations by s t e r i c crowding, which i s consistent with previous molecular mechanics studies (13,17). I f the i n t e r n a l geometry of the rings and sidechains i s not allowed to relax as φ and φ are changed, then the c r y s t a l geometry i s e s s e n t i a l l y the only possible conformation, due to s t e r i c overlaps. Having thus used available experimental information i n this p a r t i c u l a r case to i d e n t i f y a reasonable low energy conformation, t h i s conformation could then be used to map out a family of related low energy conformations at nearby values of the angles φ and φ by using this c r y s t a l structure as a s t a r t i n g geometry, and rotating the structure to various adjacent values of φ and φ (^±Δ,^±Δ) and minimizing. This procedure was then extended to the next nearest (φ,ψ) g r i d points, using the newly minimized structures found i n the previous round as s t a r t i n g structures, and extended throughout the entire configuration space i f desired. As one moves farther away from the o r i g i n a l minimum structure i n quasi-radial directions i n (φ,ψ) space, i t becomes increasing more l i k e l y that some other arrangement of the various internal coordinates might a c t u a l l y lead to the lowest possible energy value at that (φ,ψ) g r i d point. Because rearrangement to any such lower energy structure could involve an i n i t i a l increase i n energy, the minimization searches might thus f a i l to f i n d these alternate conformations. After mapping out a s u f f i c i e n t region of (^,ψ) space using t h i s quasi-radial approach of exploration ( " s u f f i c i e n t " being defined as including a l l nearby conformers within some s p e c i f i e d high-energy contour), alternate structures with lower minimized energy might be sought by a r b i t r a r i l y making large changes i n various other i n t e r n a l degrees of freedom followed by a new cycle of exhaustive minimization. Such e s s e n t i a l l y random searching must be attempted not only i n the v i c i n i t y of the already located minima but also i n other regions of configuration space where



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stable minima might be possible, and p a r t i c u l a r l y i n the region of possible b a r r i e r s between conformations. Any stable minima i n (φ,ψ) space that are i d e n t i f i e d must then also be used as the seed structures for mapping out the relaxed energy of structures nearby i n (φ,ψ) space. I f these newly i d e n t i f i e d minimum-energy structures have b a s i c a l l y the same arrangement of a l l of t h e i r i n t e r n a l degrees of freedom as the previously i d e n t i f i e d low energy conformer, then t h e i r l o c a l energy surface would simply be an extension of that surface into the new region of configuration space; under i d e a l or fortunate circumstances, the extension of the former p a r t i a l or l o c a l surface throughout the f u l l configuration space would have i d e n t i f i e d these other l o c a l minima as well. As a concrete example of this procedure, consider the case of sucrose. With the CHARMM-like potential energy function of Ha et a l . (18), which probably overemphasizes intramolecular hydrogen bonding i n vacuum calculations, the hydroxyl groups around pyranoid rings a l l tend to l i n e up i n c i r c u i t s around the perimeter of the r i n g as each hydroxyl dipole attempts to hydrogen bond to i t s neighbor. These c i r c u i t s can "point" i n one of two directions around the r i n g (Figure 1), either i n the same d i r e c t i o n as the numbering of the r i n g atoms (referred to here as clockwise), or i n the opposite d i r e c t i o n (which we w i l l c a l l counterclockwise). While i n general these two conformational patterns are close i n energy, they are s t r u c t u r a l l y d i s t i n c t and thus lead to two separate "families" of possible conformational arrangements for each value φ and ψ for sucrose i n vacuum. Transitions between these two families do not occur i n vacuum since the a c t i v a t i o n energy i s large. However, i n t u i t i o n and the results of preliminary MD simulations of both glucose (19) and sucrose (unpublished work) i n aqueous solution indicate that these networks become disrupted by hydrogen bonding to aqueous solvent. Three low-energy (φ,ψ) regions were i d e n t i f i e d f o r sucrose ( c a l l e d A, B, and C.; see Figure 2). For two of these regions, complete and separate p a r t i a l or l o c a l maps could be developed which primarily d i f f e r e d only i n the d i r e c t i o n of the hydrogen bond c i r c u i t s i n the glucose residue. For the t h i r d general conformational region, only one of these arrangements was of low energy, since for that family of (φ,ψ) combinations, the opposite hydrogen bond c i r c u i t had one fewer hydrogen bond. The global minimum energy structure, which has the counterclockwise hydrogen bond pattern, and i t s associated l o c a l energy map, were labeled SI. The minimum energy conformation i n the same region (A) of (φ,ψ) space but with the opposite hydrogen bond o r i e n t a t i o n was c a l l e d S2, along with the l o c a l relaxed energy surface associated with i t . The c r y s t a l structure has a hydrogen bond pattern most c l o s e l y resembling the higher energy S2 geometry due to intermolecular c r y s t a l contacts. The clockwise geometry i n the "B" region was c a l l e d S3, and the conformation i n this same region with the opposite, counterclockwise pattern was c a l l e d S4. S5 was used to designate the sole low energy conformation i n the C region, which i s counterclockwise, along with i t s relaxed energy surface. Five separate l o c a l energy maps were developed, three of which (SI, S4, and S5) could be combined to give a complete



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Α

Β

Figure 1. Two d i f f e r e n t general orientations of the hydroxyl groups around the six-membered r i n g i n sucrose. (A) The counterclockwise orientation of the global minimum S i . (B) The clockwise orientation f o r the l o c a l minimum S2.

Φ Figure 2. The calculated adiabatic energy map f o r sucrose. Contours are indicated at 2, 4, 6, and 8 kcal/mol above the global SI minimum. The stars r e f e r to the various minima calculated with the present p o t e n t i a l energy function.



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relaxed surface, as could be done with the remaining two, which would produce a surface with only two major low-energy regions. A complete adiabatic map f o r sucrose with t h i s p o t e n t i a l energy function could then be synthesized by taking the lowest energy structure f o r each (φ,ψ) combination, regardless of from which surface i t comes, and p l o t t i n g these together, as i n Figure 2. Any such 2-dimensional energy map i s a cross section through the complex, multidimensional configurational hyperspace of a moderately large molecule l i k e sucrose, and obscures many important s t r u c t u r a l d e t a i l s . Several competing and sometimes mutually exclusive i n t e r - r i n g hydrogen bonds are p a r t i c u l a r l y important i n determining the r e l a t i v e s t a b i l i t i e s of the l o c a l minima. As an example, Figure 5a i l l u s t r a t e s those regions on the l o c a l ("partial") map around the S4 minimum where several hydrogen bonds are possible. These patterns would be d i f f e r e n t f o r the S3 map i n the same (φ,ψ) region (8). Because i t represents the lowest energy structure possible for each combination of φ and ψ, the adiabatic surface should i d e a l l y be the surface over which the disaccharide moves as i t undergoes conformational fluctuations and t r a n s i t i o n s . As such, the adiabatic surface would be e s s e n t i a l to the i n t e r p r e t a t i o n of molecular dynamics simulations of disaccharides. However, while thermodynamics guarantees that given s u f f i c i e n t time, a system w i l l inevitably relax to the lowest (free) energy state, during the course of a conformational f l u c t u a t i o n by a disaccharide, the molecule may pass through a given region of (φ,ψ) space i n a very b r i e f time (on the order of a few tens of femtoseconds i n some cases). I f the time required for the system to relax to the adiabatic surface i s long compared to t h i s timescale f o r dynamical fluctuations, then the molecule w i l l probably not relax to the adiabatic surface, but instead w i l l follow the l o c a l relaxed surface. Such a case exists for disaccharides i n vacuum using the Ha et a l . energy function (18), since the t r a n s i t i o n from one hydrogen-bonded pattern to the other (such as from clockwise to counterclockwise) i n i t i a l l y involves the simultaneous breaking of several hydrogen bonds before the opposite hydrogen-bonding pattern can be established. This s i t u a t i o n i s an a r t i f i c i a l or nonphysical one, however, since i t would not a r i s e i n aqueous solution, where no hydrogen bonds would need to be broken during a hydroxyl rotation, as alternate hydrogen bond partners would be present i n the water molecules themselves. (In fact, i n aqueous solution, such c i r c u i t s of hydrogen bonds might not form at a l l , since the hydroxyl groups could s a t i s f y t h e i r hydrogen bonding requirements by bonding with the solvent, without the entropie constraints of the intramolecularly bonded r i n g (19)). In the case of sucrose, the p a r t i a l , l o c a l surfaces are t o p o l o g i c a l l y very s i m i l a r , so that there i s l i t t l e difference between them and the actual adiabatic surface. Molecular Dynamics Simulations of Sucrose Preparation of the adiabatic energy map for sucrose revealed that while only one conformation i s allowed for this molecule i f i t i s kept r i g i d , when f l e x i b i l i t y i s taken into account, several



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r e l a t i v e l y low energy structures are possible. In order to examine the actual dynamical behavior of these conformers, and to study how t r a n s i t i o n s between these structures might occur, a series of molecular dynamics simulations were also calculated f o r sucrose using the CHARMM program (7), and were interpreted i n terms of the relaxed energy surfaces. Trajectories with d i f f e r e n t i n i t i a l v e l o c i t y assignments were computed f o r each of the l o c a l minimum energy structures located i n the three low energy regions of (φ,ψ) space (A, B, and C.; see Figure 2). The calculations were done i n the microcanonical ensemble at a temperature of 300K ± 5K. Energy was well conserved throughout the t r a j e c t o r i e s , and no o v e r a l l d r i f t s i n molecular temperature were observed. Small ensembles of t r a j e c t o r i e s (12 for SI and 6 each f o r the other minima) were calculated f o r the averaging of system properties. Each trajectory was equilibrated by v e l o c i t y reassignments during an i n i t i a l period of 20ps, followed by another 20ps of dynamics used f o r data c o l l e c t i o n . A l l possible non-bonded interactions i n these t r a j e c t o r i e s were included i n the energy calculations; that i s , no long-range truncations were applied. The d i e l e c t r i c constant f o r these calculations was taken to be unity, as was the case i n the energy mapping study. In general, these t r a j e c t o r i e s were very well described by the relaxed maps. Figure 3 shows an example of a t y p i c a l trajectory superimposed onto the corresponding p a r t i a l or l o c a l relaxed energy map; i n t h i s example, the adiabatic surface would also provide an equally good representation. As can be seen, the asymmetries i n the motions and the magnitudes of the s t r u c t u r a l fluctuations are e a s i l y understood i n terms of the energy map, and would be incomprehensible using a r i g i d r o t a t i o n energy analysis. From a d i r e c t examination of the t r a j e c t o r i e s i t i s possible to make estimates for the timescales of the various dynamical processes which occur i n these molecules i n the course of normal thermal fluctuations. Figure 4 i l l u s t r a t e s the v a r i a t i o n with time of the dihedral angle C5g-C6g-06g-H'6g as calculated from two d i f f e r e n t molecular dynamics simulations. As can be seen from t h i s figure, the dynamical behavior can vary somewhat with the simulation conditions; i n one simulation this i n t e r n a l coordinate exhibited frequent and very fast changes i n conformation with durations of less than 0.1 ps, while i n the other case two of these conformers were more metastable, with l i f e t i m e s of about 1 ps, and with a steady o s c i l l a t i o n between the two states and longer times required to accomplish the t r a n s i t i o n s . Figure 5 i l l u s t r a t e s the competition between two possible hydrogen bonds consistent with the S4 family of conformations. Figure 5a i s a superposition upon the l o c a l relaxed energy map of the regions where the H'2g...03f and H'2g...06f hydrogen bonds are possible. As can be seen from this figure, these two hydrogen bonds are mutually exclusive, and as the H'2g hydrogen atom makes a hydrogen bond with one of these acceptors, i t must break i t s hydrogen bond with the other. Figures 5b and 5c show that the exchange expected from the l o c a l energy map does indeed occur. Three exchanges were observed i n this simulation; from an ensemble of such simulations, or from a single simulation of much greater duration, i t would be


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0.0 h

60.0 h

120.0 -100.0 -60.0

-20.0

20.0

60.0

100.0

0 Figure 3. An example of a sucrose trajectory i n (φ,φ) space superimposed upon the l o c a l relaxed or p a r t i a l conformational energy map (S2).

0.0

8.0

20 0

12 0 Time (ps) β

β

Figure 4a. Fast oscillations between the three stable orientations (60 *, -60 , 180 ).


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180 0 ι

1

1

Γ

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1200

120 0 1B0.0 '

1

oo

1

io

1

no

120

1

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200

Time (ps) Figure 4b. Slower oscillation between longer-lived metastable conformers at 60 * and -60 *.

Μ·2·

Η

Figure 4c An example of different timescales for motions in the dihedral angle C5g-C6g06g-H'6g (indicated in the molecular sketch) as calculated in two separate molecular dynamics simulations.


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S4 map f

H29...03 domain

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120.0 -100.0 -60.0

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Φ Figure 5a. An example of a partial energy map, the local relaxed map for the S4 family of conformations. Contours are indicated at 4, 6, and 8 kcal/mol above the global SI minimum, which does not appear on this map. The dashed lines surround the different inter-residue hydrogen bond domains (with a cutoff criterion of 2.05Â for the Ο . . . Η distance), with the tic marks on the dashes pointing toward the region where the given hydrogen bond is allowed.

Figure 5b. History of the fluctuations in the hydrogen bond distance H'2g . . . 03f as calculated from a molecular dynamics trajectory.


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8.0 h

8.0 h


i 3

4.0 h

2.0

4.0

8.0

12.0

18.0

Time (ps) Figure 5c. History of the H'2g . . . 06f hydrogen bond distance, as calculated from the same trajectory.

possible to estimate a t r a n s i t i o n frequency. From Figure 5 i t can be seen that the actual t r a n s i t i o n takes place rather slowly, taking as much as a picosecond to complete each time i t occurs. Transitions between major conformational wells f o r the sucrose molecule are rare i n vacuum on the picosecond timescale, although one t r a n s i t i o n was observed i n these simulations. Figure 6 i l l u s t r a t e s a trajectory which began i n the S3 conformation and underwent a t r a n s i t i o n to the lower energy S2 conformation midway through the simulation. This t r a n s i t i o n , the only one observed i n a t o t a l of 720 ps of dynamics i n 36 separate t r a j e c t o r i e s , occurred between the two forms predicted by Christofides and Davies (15) to occur i n DMS0. As can be seen, the course of the t r a n s i t i o n i s well described by the topology of the energy surface, and the approximate path could be e a s i l y predicted i n advance from this map. In the figure, the t r a n s i t i o n i s shown superimposed on the combination of the S2 and S3 l o c a l maps, rather than the adiabatic surface. While the topological differences between these two surfaces are again small, i t i s worthwhile to note that the S2 structure i s not the lowest energy form i n the central well, and that the molecule d i d not at any time during or a f t e r this t r a n s i t i o n relax to t h i s SI conformer, with i t s opposite pattern f o r the pyranoid hydrogen bond c i r c u i t . Neither d i d any of the t r a j e c t o r i e s started i n the S2 conformation make a t r a n s i t i o n to the S i form. This s t a b i l i t y indicates that the timescale for such a relaxation to the true adiabatic surface i s indeed much longer than the timescale f o r conformational fluctuations and transitions f o r this molecule i n vacuum.


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0

0

ι—I

f

\

ι—ι—ι—ι—ι—Γ

Figure 6. A molecular dynamics t r a j e c t o r y which underwent a t r a n s i t i o n from the S3 to the S2 conformation, superimposed on the relaxed surface created by combining the S2 and S3 surfaces. At the bottom are i l l u s t r a t i o n s of the molecular geometry i n the beginning and f i n a l conformations.

Conclusions A complete understanding of the structures and motions of carbohydrates w i l l require including f l e x i b i l i t y i n the conformational energy descriptions of disaccharides which are frequently used to model polymers b u i l t from sugar monomers. In p a r t i c u l a r , understanding the dynamics of disaccharides w i l l necessitate the production of relaxed energy maps of one form or another which take into account the i n t e r n a l s t r u c t u r a l readjustments i n monomer units as the g l y c o s i d i c angles change. Because intramolecular reorganization rates are frequently slow compared to the dynamics timescale, the most useful energy surface


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for describing disaccharide conformations might not be the adiabatic map but a relaxed surface i n which the minimizations progress outward from i d e n t i f i e d l o c a l minima i n a quasi-radial manner, proceeding from structure to structure i n roughly the same sequence as might occur during a r e a l conformational fluctuation. I t should also be remembered, as i l l u s t r a t e d by the a r t i f a c t s i n the sucrose studies, that vacuum calculations could p o t e n t i a l l y be inadequate. Most carbohydrates are found i n aqueous environments, and the influence of solvent upon conformation might be s i g n i f i c a n t . Since physical properties are determined by free energies rather than mechanical energies, i t may be necessary i n some cases to compute (φ,φ) maps of the potential of mean force from solution MD studies, which would include the solvent contribution. Acknowledgments This work was supported i n part by NIH grant GM34970 and USDA Hatch project 143-433, and by a grant of travel funds (to V.H.T.) from INRA. Literature Cited 1. 2.

Brant, D.A. Ann. Rev. Biophys. Bioeng. 1972,1,369. French, A.D.; Murphy, V.G. Carbohydr. Res. 1973,27,391; Polymer 1977,18,489. 3. Ha, S.N.; Madsen, L.J.; Brady, J.W. Biopolymers 1988,27,1927. 4. Tran, V.; Buleon, Α.; Imberty, Α.; Perez, S. Biopolymers 1989,28,679. 5. Gelin, B.R.; Karplus, M. J. Am. Chem. Soc. 1975,97,6996. 6. Brooks, C.L.; Karplus, M.; Pettitt, B.M. Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics; Advances in Chemical Physics, Wiley -Interscience: New York, 1988, Vol. LXXI. 7. Brooks, B.R.; Bruccoleri, R.E.; Olafson, B.D.; States, D.J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983,4,187. 8. Tran, V.H.; Brady, J.W. Biopolymers in press. 9. Tran, V.H.; Brady, J.W. Biopolymers in press. 10. McCammon, J.Α.; Harvey, S.C. Dynamics of Proteins and Nucleic Acids; Cambridge University Press, Cambridge, 1987. 11. Brown, G.M.; Levy, H.A. Acta Crys. 1973,B29,790. 12. Hanson, J.C.; Sieker, L.C.; Jensen, L.H. Acta Crys. 1973,B29,797. 13. Bock, K.; Lemieux, R.U. Carbohydr. Res. 1982,100,63. 14. McCain, D.C.; Markley, J.C. J. Am. Chem. Soc. 1986,108,4259. 15. Davies, D.B.; Christofides, J.C. Carbohydr. Res. 1987,163,269. 16. Mathlouthi, M.; Luu, C.; Meffroy-Biget, A.M.; Luu, D.V. Carbohydr. Res. 1980,81,213. 17. Ferretti, V.; Bertolasi, V.; G i l l i , G. Acta Cryst. 1984,C40,531. 18. Ha, S.N.; Giammona, Α.; Field, M.; Brady, J.W. Carbohydr. Res. 1988,180,207. 19. Brady, J.W. J. Am. Chem. Soc. 1989,111,5155. RECEIVED March 21, 1990


Computer Modeling of Carbohydrate Molecules - American Chemical

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