Computer Modeling of Carbohydrate Molecules - ACS Publications

Chapter 9

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 13, 2016 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch009

Solvent Effects on Conformation of Carbohydrates Molecular Dynamics Simulation of Sorbitol, Mannitol, and Methoxytetrahydropyran J. Raul Grigera Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB), University of La Plata, c.c. 565, 1900 La Plata, Argentina Molecular dynamics (MD) simulations show that the conformations of sorbitol and mannitol depend on the type of solvent. The predicted conformations agreed well with experiment, supporting the view that MD has a good predictive value for solutions of carbohydrates. Preliminary dynamics results for methoxy-tetrahydropyran (MTHP) show that the methoxy group moves more in water than in vacuum. Molecular conformation i s highly related to functional properties. Since the conformation of the c r y s t a l l i n e s o l i d s can be p r e c i s e l y determined by d i f f r a c t i o n methods, molecular modeling i s most important f o r interpreting molecular structures i n solution. This i s , however, even more d i f f i c u l t for theoreticians. While carbohydrates dissolve i n a v a r i e t y of solvents, the important solvent f o r b i o l o g i c a l systems i s water and t h i s solvent deserves special emphasis. Molecular dynamics (MD) simulation have been used for several years to get information on both equilibrium and dynamical conditions of various systems, including solutions of complex molecules. However, only a few carbohydrates have been studied (1-3). Sorbitol and mannitol represent a p a i r of hexytols that d i f f e r only i n the configuration of one hydroxy group at C2. This s l i g h t difference i n t h e i r configurations gives both compounds d i f f e r i n g physicochemical properties. For example, s o r b i t o l i s three and one h a l f times more soluble than mannitol i n water. Previous MD simulation of these hexytols (2) pointed out some c h a r a c t e r i s t i c s that warrant further discussion. In p a r t i c u l a r t h e i r conformations depended on the solvent system. In t h i s work we discuss further the previous r e s u l t s from simulations of s o r b i t o l and mannitol and compare them with new calculations and recent experimental data. We also present some preliminary data f o r methoxy-tetrahydropyran (MTHP) i n vacuo and in water. 0097-6156/90/0430-0152$06.00/0 © 1990 American Chemical Society

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

9.

GRIGERA

Solvent Effects on Conformation of Carbohydrates 153


Methods Computer Simulation. The GROMOS package (Biomos n.v. Groningen) was used f o r the MD simulations. Equations of motion were integrated using a leap-frog algorithm at a time i n t e r v a l of 2 fms. A thermal bath and a hydrostatic pressure system kept the pressure and temperature of the main system constant. This constant-temperature, constant-pressure procedure i s part of the o r i g i n a l GROMOS package. The SHAKE procedure held constant the fixed distances i n the model. A l l data reported are from runs made a f t e r e q u i l i b r a t i o n . The precise time to a t t a i n equilibrium was not determined but e q u i l i b r a t i o n was monitored both by the d r i f t of t o t a l energy and the s t a b i l i t y of the system density. The simulation boxes were cubes ( f o r both hexytols) or a truncated octahedron ( f o r MTHP). The VAX 11/750 of the IFLYSIB performed the main calculations. Graphic displays were produced with a personal computer and ALCHEMY software (Tripos Inc., St. Louis). Force F i e l d . Only atom-atom interactions were considered i . e . bond lengths and bond angles were taken as r i g i d . No e x p l i c i t t o r s i o n a l potential was used, so the energy changes with change i n torsion angle r e s u l t only from the e l e c t r o s t a t i c and the van der Waals forces of the atoms involved. We adopt t h i s p o s i t i o n since we consider that a predefined t o r s i o n a l potential may bias the conformation. The parameters f o r the force f i e l d are GROMOS based, although the p a r t i a l charges have important differences. For s o r b i t o l and mannitol the parameters were from Ref. 2 while those f o r MTHP are described i n Table V below. Our parameters correspond to a set devised to be used with the e x p l i c i t addition of water i f water i s to be considered. While we cannot exclude the p o s s i b i l i t y that some information from solution has inadvertently been included i n those parameters, we believe that the isolated molecule w i l l be reproduced i f solvent i s not e x p l i c i t l y present. Solvent. The water molecules conformed to the Simple Point Charge Extended model (SPC/E) (4), which i s summarized i n Table I. The non-polar' solvents were taken as monoatomic non-charged atomic l i q u i d s with the same Lennard-Jones (6-12) parameters as oxygen i n water, making an argon-like solvent. Table I. P r i n c i p a l features of SPC/E Water Model

0-H bond H-O-H angle A (oxygen centered) Β (oxygen centered) Oxygen charge Hydrogen charge

0.1 nm 109 -3 6 2.6169 X 10 /(nm .kJ/mol) -6 12 2.6332 X 10 /(nm .kJ/mol) -0.8476 e 0.4238 e


154

COMPUTER MODELING OF CARBOHYDRATE MOLECULES S o r b i t o l and Mannitol I n i t i a l l y , the hexytols have planar zig-zag conformations with C-0 bond lengths of 0.143 nm, C-C bond lengths of 0.152 nm, CCC angle of 113° and CCO angle of 110! A l l of these parameters are based on crystallographic information (5).


Results Table II shows the average end-to-end distance over 20 ps f o r mannitol and s o r b i t o l i n vacuuo and i n solution of an argon-like (L-J) solvent and SPC/E water. The average lengths a l l indicate s i c k l e shapes, except f o r mannitol i n water which i s f u l l y extended. This points to a s p e c i f i c solute-solvent i n t e r a c t i o n between mannitol and water, not just an unspecific solvent e f f e c t that i s not present i n solvent other than water. The model non aqueous solvent i s very a r t i f i c i a l , but i t should represent the main features of the class of non-polar, s p h e r i c a l l y symmetric solvents. Table I I .

Average End-to-End Distances f o r S o r b i t o l and Mannitol Isolated Molecule

Mannitol Sorbitol

L-J

0.53 0.55

Solvent

SPC/E Water

0.52 0.56

0.64 0.55

(nm)

Figure 1 shows the t r a j e c t o r i e s f o r the end-to-end distances for s o r b i t o l and mannitol i n water and mannitol the L-J solvent. The smaller fluctuations i n end-to-end distance of mannitol i n water might be interpreted i n terms of lowered mobility of the molecule. However, Figure 2 shows that there are s t i l l large fluctuations i n the torsion angles during the simulation. Therefore, the i n t e r n a l mobility i s high, although compensating changes i n torsion angles keep the f i n a l distance rather constant. Table III shows the computed proton-proton scalar (J-J) coupling, along with experimental values. Coupling constants have been computed by using the Karplus formula i n the form ι

J = -1.4 cos

φ

+ 9.4 cos

# + 1.6

(1)

They agree q u a l i t a t i v e l y , confirming the predictive c a p a b i l i t y of the method. Hydration. Some dynamic c h a r a c t e r i s t i c s of hydration can be obtained from these simulations. According to Samoilov (7,8) we define the "hydration time r a t i o ' R as the r a t i o between the average time that a water molecule spends near the solute (ts) and the average time that water molecules spend near to other water molecule (tw); i . e . R=ts/tw. The "hydration number' here i s defined as the number of water molecules that remain, on the average, around a solute molecule at a prescribed distance (0.425 nm i n t h i s case).



GRIGERA

Solvent Effects on Conformation of Carbohydrates

Φ/deg

sorbitol

180 -I

90

18 Time/ps

Figure 1. T r a j e c t o r i e s of t o r s i o n angles gll (C1-C2-C3-C4); (C2-C3-C4-C5) and 03 (C3-C4-C5-C6) f o r mannitol and s o r b i t o l during 20 ps simulation.


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COMPUTER MODELING OF CARBOHYDRATE MOLECULES Table I I I . NMR Proton Coupling Constants f o r Mannitol and S o r b i t o l i n Water


J

H H H H H H H

Mannitol

1* ,2 1, 2 2, 3 3, 4 4, 5 5, 6 6, 6'

Sorbitol

cale.

exp(a)

8.543 1.976 11.411 1.633 5.382 3.917 5.441

6.426 2.935 8.990 1.021 -

-

cale.

exp(b)

5.078 4.240 4.685 1.562 9.855 1.617 9.759

6.55 3.55 5.90 1.7 8.25 2.95 6.3

exp(c) 6.55 4.25 6.0 2.47 7.70 3.33 6.24

a) Franks et a l . ( 9 ) , b) Hawkes and Lewis (6), c) D.B. Davies (quoted i n Réf. 9). Table IV shows the values f o r both polyols. The hydration numbers are a consequence of molecular shape. Following Samoilov, we c l a s s i f i e d both compunds as "negatively hydrated since t h e i r hydration time r a t i o s are less than one, with s o r b i t o l being more negatively hydrated. Table

IV.

Hydration Numbers and Hydration Time Ratio f o r S o r b i t o l and Mannitol

Hydration Number Sorbitol Mannitol

11.45 13.22

Hydration Time Ratio(R) 0.39 0.80

Although the concept of negative hydration was advanced by Samoilov several years ago (7), the idea that an interacting group might increase the mobility of surrounding water i s not e a s i l y accepted. When considering the i n d i v i d u a l atoms of the hexytol, the water residence times vary from atom to atom. While the water residence times for some atoms (e.g. 03 and 04 of mannitol) are high, the average over the whole molecule i s a r a t i o of less than one. It might be suspected that a single solute, for which the s t a t i s t i c s are c e r t a i n l y poor, could have a l o c a l temperature higher than the average, producing an a r t i f i c i a l l y larger mobility in the neighborhood of the solute. In our case we have eliminated that p o s s i b i l i t y by using a separate temperature s c a l i n g f o r solute and solvent. Recent 620.6 MHz nmr r e s u l t s on s o r b i t o l and mannitol (9) confirm that s o r b i t o l rotates more f r e e l y i n water than mannitol. This suggests that there i s less solute-solvent interaction i n s o r b i t o l . Calorimetric r e s u l t s (10) predict that s o r b i t o l and mannitol should have hydration behavior s i m i l a r to that described above. Those workers, however, referred to "structure breaking' properties, even though no s t r u c t u r a l data was obtained.



9.

GRIGERA

Solvent Effects on Conformation of Carbohydrates

0.45 J 0

.

• 6

12

157

18

Time/pe Figure 2. Time evolution of the end-to-end distance of :([])sorbitol i n water; (X)mannitol i n water; fo) mannitol i n a LJ solvent. MTHP Methoxytetrahydropyran (MTHP) (Figure 3) has received considerable attention as a simple substitute f o r the glycosides i n hydration studies (11-13). In our i n i t i a l studies of the a x i a l anomer, we kept the r i n g r i g i d , as well as the bond lengths of the methoxy group. In order t o further reduce the time required f o r the calculations, we used "united atoms" f o r CH, CH2 and CH3. P a r t i a l charges f o r the united atoms were the sum of the i n d i v i d u a l components given by Mardsen et a l . (14). This lowers the dipole moment of the model composed of united atoms, compared to the experimental value. (See Table V.) Table V. Interaction Parameters for MTHP United atom group name CI C2 C3 C4 C5 C6 01 05

(CG) (CR) (C*) (C*) (CS) (CM) (0G) (OS)

CH CH2 CH2 CH2 CH2 CH3 0 0

Q/e

0.207 0.000 0.000 0.000 0.066 0.141 -0.282 -0.132

6 1/2 [A/(Kcal.nm /mol] 228.98 193.98 193.98 193.98 193.98 193.22 96.72 96.72

X X X X X X X X

10 10 10 10 10 10 10 10

-3 -3 -3 -3 -3 -3 -3 -3

12 1/2 [B/(Kcal.nm /mol] 17.2265 12.0887 12.0887 12.0887 12.0887 10.4000 1.7514 2.2880

X X X X X X X X

10 10 10 10 10 10 10 10

-3 -3 -3 -3 -3 -3 -3 -3

The LJ parameters f o r the X-Y i n t e r a c t i o n are obtcined by the product of the parameter of the table f o r each ate n. Again, no e x p l i c i t t o r s i o n a l potentials were used. Figure 4 shows the p o t e n t i a l energy a r i s i n g only from the atom-atom interactions f o r charges i n the t o r s i o n angle 05-C1-01-C6 i n the absence of solvent. Structure. We have simulated MTHP i n i s o l a t i o n and i n an i n f i n i t e l y d i l u t e d aqueous solution (56 water molecules i n a truncated octahedron). The average p o s i t i o n value of ύ (01-C105-C6) i s 8 5 i n i s o l a t i o n and 75°in water. Previous calculations e



158

COMPUTER MODELING OF CARBOHYDRATE MOLECULES

using energy minimization techniques (15J found several allowed conformers for r i g i d , axial MTHP. Let us consider the results of Mardsen et a l . (14) as representative. The least energetic conformer has 0 of 60°, and the next two 0 of 120° and 180°. In the static description of the system, as obtained by energy minimization, the relative populations of the three conformers are determined after consideration of their relative energies and the height of the barriers. This may give a clearer idea of the average conformation. In our dynamics simulation, we have a time average that includes excursions to the different conformers. If both methods are reliable, our average φ value should be closer to the least energetic conformer from the static study than to any other. Our "solution' value i s closer to the 60° mininimum from the statics study. Forcefields such as used by Mardsen et a l . are solution equivalent' ( i . e . contain information on the interactions in aqueous solution). Therefore, their results are not for a truly isolated molecule, but might be expected to be equivalent to our solution model. To allow determinations of conformation in vacuum and other solvents, water information should not appear in the basic potentials. The presence of water information in force fields i s a common problem. Dynamics. The mobility of the methoxy segment differs for the isolated and solution states. Figure 5 shows the trajectories of the 0 angle in both, with differing average values and ranges of fluctuation. While models of sorbitol and mannitol showed decreased mobility in water compared to vacuum, the methoxy group of MTHP is more mobile in water than i n vacuum. Since we used only one solvent, we cannot distinguish between unspecific solvent effects or water-dependent properties. Hydration. Since we have a detailed dynamics study with explicit water molecules we can describe the hydration of MTHP. Using the definitions developed above, we have a hydration number of 13.6 and a hydration time ratio of 1.42, i f the cut-off radius is 0.425 nm, 05-C5 and 01-C6 have the highest residence times and hydration numbers. The reason that carbon atoms are apparently favored for hydration is that we check the proximity of water molecules by the distance to the water oxygen. Some hydrogen bonds to 01 and 05, for example, give very close proximity of water oxygen to the neighboring carbons atoms. Thus, the criterion for hydration of the atoms is met but there may not actually be any strong interaction between the solvent and the carbon atoms. The hydration values for MTHP are different than those for sorbitol and mannitol. This i s not surprising since most molecular properties are quite different. This result depends on the model since a l l were studied with the same simulation procedure. Figure 6 shows a molecule of MTHP and some water molecules around i t . This picture is a snapshot; not an average. This picture gives some gross features of the hydration but from i t alone we cannot assign well-defined positions and orientations of the water molecules. Even so, the hydration structure compares, at least qualitatively, well with the one proposed by Tvaroska and Kozar (15). For easy comparison we have used the same labels as In Computer Modeling of Carbohydrate Molecules; French, Alfred D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

9.

Solvent Effects on Conformation of Carbohydrates 159

GRIGERA

CA(CH ) 2


01

Figure 3. Molecular structure and labeling of MTHP. 30 Γ

-10 I

ι 60

ι 90

1 120

1 150

φ/deg Figure 4. Potential of the torsional angle 0 in MTHP produced by the atom-atom interaction.

Φ/deg

30 4

* 0

i

s 4

i

1 8

1

γ12

Time/ps

Figure 5. Trajectories of the angle 0 during simulation of MTHP in isolation (X) and i n aqueous solution(O).



160

COMPUTER MODELING OF CARBOHYDRATE MOLECULES

5a

C5

5b

Figure 6. A MTHP molecule and the nearest water molecules. The picture corresponds to a single MD configuration and not to an average configuration. Water molecules are labeled as i n Figure 2 of Ref. 15.


9. GRIGERA Solvent Effects on Conformation of Carbohydrates

161161

i n Réf. 15 f o r the four water molecules shown there. The r e s u l t s for MTHP are s t i l l preliminary, and several aspects, such as molecular f l e x i b i l i t y and other solvents, must be considered before the study i s finished. These simulations are underway i n our laboratory.


Conclusions These examples of simulations of the molecular dynamics of carbohydrates show the p o s s i b i l i t y of predicting t h e i r behavior i n d i f f e r e n t solvents. Experimental work has confirmed these findings. While t h e o r e t i c a l prediction i s becoming more r e l i a b l e , i t i s only q u a l i t a t i v e and we must consider the t h e o r e t i c a l r e s u l t s within the framework of the actual c a p a b i l i t y of the methods. Current minicomputers allow simulation of large system. Polysaccharides, f o r instance, are being studied by t h i s technique. However, the description of carbohydrate solutions i s s t i l l poor, and simple systems can help i n the understanding of the problems. Acknowledgments This work was p a r t l y supported by the Consejo Nacional de Investigaciones C i e n t i f i c a s y Tecnicas of Argentina (CONICET) by grant PID 3-056100/88. I am member of the Carrera d e l Investigador of CONICET. I wish to thank Profs. H. J . Berendsen and W. van Gunsteren f o r granting permission f o r the use of GR0M0S and Prof. F. Franks for providing experimental data p r i o r to publication. The interest of Prof. J . W. Brady i n the work i s g r a t e f u l l y acknowledge. The useful comments and the help i n the f i n a l writing made by Dr. A. D. French ( f a r beyond h i s task as editor) deserves special thanks.

Literature Cited 1. Brady J.W. J. Am. Chem. Soc. 1986, 108, 8153. 2. Grigera J.R. J.Chem.Soc. Faraday 1 1988, 148, 2603. 3. Kohler J. Disseration. Berlin 1987. Kohler J.; Saenger W; van Gunsteren W.F. Eur.Biophys.J. 1988, 16, 153. J. Biomol. Struct. Dyn. 1988, 6, 181. 4. Berendsen H.J.C.; Grigera J.R.; Straatsma T. J. Phys. Chem. 1987, 91, 6269. 5. Jeffrey G.A.; Kim H.S. Carbohydr. Res. 1970, 14, 207. 6. Hawkes G.E.; Lewis D. J. Chem. Soc. Perkin Trans. II, 1984, 2073. 7. Samoilov O. Ya. Disc. Faraday Soc. 1957, 24, 141. 8. Samoilov O. Ya. Structure of Aqueous Electrolyte Solutions and Hydration of Ions. Consultants Bureau, New York, 1965. 9. Franks F.; Dadok J.; Kay R. L. unpublished. 10. Wilson D. R.; Wen-Yang W. J. Phys. Chem. 1976, 80, 413. 11. Kozar T.; Tvaroska I. Theor. Chim. Acta 1979, 53, 9. 12. Tvaroska I.; Kozar T. J. Am. Chem. Soc. 1980, 102, 6929. 13. Tvaroska I. Carbohydr. Res. 1984, 125, 155. 14. Mardsen A.; Robson B . ; Thompson J.S. J. Chem. Soc. Faraday 1 1988, 84, 2519. 15. Tvaroska I.; Kozar T. Internatl. J. Quantum Chem. 1983, 23, 765. RECEIVED February 13, 1990 In Computer Modeling of Carbohydrate Molecules; French, Alfred D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

Computer Modeling of Carbohydrate Molecules - ACS Publications

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