kony2002.pdf

An Improved OPLS–AA Force Field for Carbohydrates

D. KONY,1 W. DAMM,2 S. STOLL,1 W. F. VAN GUNSTEREN2

1CABE, Department of Inorganic, Analytical and Applied Chemistry, Science II, University ofGeneva, 30 Quai E. Ansermet, CH-1211 Geneva 4, Switzerland

2Laboratory of Physical Chemistry, ETH Zurich, ETH Honggerberg,CH-8093 Zurich, Switzerland

Received 6 September 2001; Accepted 16 May 2002Published online XX XXXX 2002 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcc.10139

Abstract: This work describes an improved version of the original OPLS–all atom (OPLS–AA) force field forcarbohydrates (Damm et al., J Comp Chem 1997, 18, 1955). The improvement is achieved by applying additionalscaling factors for the electrostatic interactions between 1,5- and 1,6-interactions. This new model is tested first forimproving the conformational energetics of 1,2-ethanediol, the smallest polyol. With a 1,5-scaling factor of 1.25 theforce field calculated relative energies are in excellent agreement with the ab initio-derived data. Applying the new1,5-scaling makes it also necessary to use a 1,6-scaling factor for the interactions between the C4 and C6 atoms inhexopyranoses. After torsional parameter fitting, this improves the conformational energetics in comparison to theOPLS–AA force field. The set of hexopyranoses included in the torsional parameter derivation consists of the twoanomers of D-glucose, D-mannose, and D-galactose, as well as of the methyl-pyranosides of D-glucose, D-mannose.Rotational profiles for the rotation of the exocyclic group and of different hydroxyl groups are also compared for thetwo force fields and at the ab initio level of theory. The new force field reduces the overly high barriers calculated usingthe OPLS–AA force field. This leads to better sampling, which was shown to produce more realistic conformationalbehavior for hexopyranoses in liquid simulation. From 10-ns molecular dynamics (MD) simulations of �-D-glucose and�-D-galactose the ratios for the three different conformations of the hydroxymethylene group and the average 3JH,H

coupling constants are derived and compared to experimental values. The results obtained for OPLS–AA–SEI force fieldare in good agreement with experiment whereas the properties derived for the OPLS–AA force field suffer fromsampling problems. The undertaken investigations show that the newly derived OPLS–AA–SEI force field will allowsimulating larger carbohydrates or polysaccharides with improved sampling of the hydroxyl groups.

© 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1416–1429, 2002

Key words: carbohydrates; 1,2-ethanediol; hexopyranoses; conformational analysis; force field; molecular dynamics

Introduction

Polysaccharides as well as even simple monosaccharides are chal-lenging molecules to model due to their numerous highly flexibleand polar OH groups. By forming intra- and intermolecular hy-drogen bonds these groups determine the conformational spacesampled.1 Using a simple force field with atom centered charges isa necessary compromise in accuracy for performing time consum-ing molecular dynamics (MD) studies in which the solvent istreated explicitly.2

The force fields available to study biomolecular systems consistof very similar potential energy functions, and are converging tothe same approach regarding the derivation of force field param-eters. The nonbonded parameters are adjusted to reproduce thephysical properties of pure liquids such as the heat of vaporizationand the density. Following this approach, it is necessary to repre-sent the polarized liquid state in an average way. This is achieved

by using 10–20% larger charges than necessary to reproduce thegas phase molecular dipole moments.3,4 The torsional parametersare fit to reproduce the gas phase conformational energetics, usu-ally derived with ab initio methods, of fragments or model systemsrepresenting the chemical environment of the torsional angle underconsideration. This allows incorporating stereoelectronic effects inthe otherwise pure mechanical force field model. The force fieldsderived with these two key elements have been found to obtainexcellent free energies of solvation and free energies of binding.5

Correspondence to: W. F. van Gunsteren; e-mail: [email protected]

Contract/grant sponsors: Swiss National Reserach Project; contract/grantnumber: 2100-0621750.00/1

Contract/grant sponsor: University of Geneva

© 2002 Wiley Periodicals, Inc.

Force field parameter developments for studying carbohydratesin the condensed phase are rare6–15 in comparison to parameterdevelopments for proteins and other simple organic molecules.The latest AMBER13 force field uses partial charges generatedfrom a least-square fit to an ab initio calculated electrostaticpotential, which is done for multiple D-glucose conformations(RESP fitting).16 When only two glucose conformations are usedfor the fitting a larger partial charge (O: �0.68 e, H: 0.46 e) isobtained on oxygen atoms of hydroxyl groups, whereas when 12conformations are used smaller charges (O: �0.54 e, H: 0.37 e) areobtained. The charge set with the smaller charge on oxygen atomsis then used for the derivation of torsional parameters and in liquidsimulations. The larger charge is in the order of a partial chargeused on a hydroxyl oxygen atom in the AMBER or the OPLS–AA17 force fields for simple monofunctional alcohols. The smallercharge assigned to carbohydrates will therefore lead to smallerinteraction energies and therefore also to weaker solvation andbinding. This could lead to artifacts in studies where a carbohy-drate is bound to a receptor with several monofunctional hydroxylgroups.

The nonbonded parameters for carbohydrates of the OPLS–AAforce field are derived by studying the liquid properties of 1,2-ethanediol.18 With these parameters the experimental values forthe heat of vaporization and density of the pure liquid are repro-duced. The charges on the hydroxyl functionality (O: �0.7 e, H:0.435 e) are slightly larger than those of monofunctional alcohols(O: �0.683 e, H: 0.418 e). Even larger charges had to be used todescribe the pure liquid properties of glycerol (O: �0.73 e, H:0.465 e).19 This indicates that the longer the polyolic chain of themonomer is, the larger the polarization effects in the pure liquidbecome. The magnitude of these charges are all within the range ofthose obtained from HF/6-31G* CHELPG fittings to reproduce theelectrostatic potential and therefore similar to those of the GLY-CAM force field.12 The torsional parameters of the OPLS–AAforce field9 are also fit to reproduce the conformational energeticsderived with ab initio calculations. In contrast to the latest AM-BER force field13 not only D-glucose but also D-galactose andD-mannose are used to obtain a wider applicable set of parameters.

The derivation of the torsional parameters for the CHARMMforce field14 follows a different concept. Only fragments, such as1,2-ethanediol or hydroxymethanol, featuring the chemically dif-ferent torsional environments of a hexopyranoses are used. How-ever, it is questionable if with those torsional parameters theconformational energetics of intact hexopyranoses can be repro-duced.

Force field parameters have also been tested and refined againstcrystal structure data.7,8 To successfully predict crystal structures,the intermolecular interactions have to be in balance with theintramolecular interactions and refined to describe the condensedphase accurately. van Eijck and Kroon developed a program (UP-ACK) for the generation of crystal structures by means of energyminimization, and have recently compared the results of three allatom force fields with geometric and energetic criteria.8 TheOPLS–AA was heralded as the most promising all-atom forcefield. This indicates that the energetics described with the OPLS–AAforce field is already rather refined. Unfortunately, these investi-gations do not give any information about the dynamical behavior.

Despite the promising results obtained for the OPLS–AA forcefield so far, large discrepancies in reproducing the gas phaserelative energies are found as well. The relative energies of the twoconformations with which the exo-anomeric effect is represented,cannot be reproduced (Fig. 1).9 A large energy discrepancy ofabout 4 kcal/mol is also observed when the two 1,2-ethanediolconformations are considered which represent the same differencein geometry. One factor contributing to this discrepancy originatesfrom the fact that the electrostatic 1,4-interactions are reduced bya factor two, which causes an imbalance with the 1,5-interactions(Fig. 1). The discrepancy between the force field and the ab initiocalculated relative energy is caused by the inclusion of the meanfield approximation used to describe the polarized liquid state.With smaller charges on the hydroxyl functionality the ab initiogas phase energetics could be much better reproduced, whereaswith the larger charges as derived for glycerol the discrepancy isincreased. The too high energy of nonhydrogen bonded structuresas shown in Figure 1 for 1,2-ethanediol lead in hexopyranoses tovery high barriers for rotation of the hydroxyl group, which leadsto sampling problems in Monte Carlo simulations using explicitsolvent.20 Such sampling problems make it impossible to accu-rately study the conformational behavior of carbohydrates.

The OPLS–AA force field has also been used to study theconformational space of �-D-Manp-(1-�3)-�-D-Glcp-Ome disac-charide in explicit water and DMSO.21 The same systems werealso run with the GLYCAM force field for carbohydrates forwhich similar results are obtained. Surprisingly, no sampling prob-lems are reported using the OPLS–AA force field. Rather, fastoscillations between g� and g� conformations with respect to theHCOH torsions are observed.

Figure 1. Conformational energies for 1,2-ethanediol and �-D-galac-tose for which the largest deviation between the OPLS–AA force fieldand the ab initio level of theory is obtained.

Improved OPLS–AA Force Field for Carbohydrates 1417

In this article we describe the development of a new version ofthe OPLS–AA force field for carbohydrates. We are aiming toimprove the largest discrepancies of the conformational energeticsobtained for the OPLS–AA force field and to better reproduce thehigh energy conformations with broken intramolecular hydrogenbonds which are populated most in aqueous solution. This is doneby applying an additional scaling factor for the 1,5- and specific1,6-interactions, which reduce the strength of the electrostaticinteractions in hexopyranoses and 1,2-ethanediol. Because theseadditions change the strength of the intramolecular nonbondedinteraction, the torsional parameters are reoptimized. The resultingparameter set is then tested in the liquid phase for obtaining bettersampling and for reproducing experimentally derived 3JH,H cou-pling constants. With an improved sampling obtained for hexopy-ranoses, larger carbohydrates could be studied by simulating forseveral nano- or microseconds in explicit solvent as has beensuccessfully done for peptides22 and proteins.23 The liquid phasesimulations reported here demonstrate that the improved gas phaseenergetics of the newly developed force field leads to a morerealistic solvation and conformational behavior of hexopyranosesin aqueous solution.

Computational Methods

Ab initio and Density Functional Theory (DFT)Calculations

Ab initio and DFT calculations are performed using the GAUSS-IAN94 program.24 For 1,2-ethanediol, all structures are optimizedat the B3LYP/6-311�G** level of theory. It has been found forthis molecule that B3LYP/6-311G** gives similar results to thoseobtained using a very high level of quantum theory.25,26 Introduc-tion of a diffuse function into the basis set, which significantlyreduces the basis set superposition error (BSSE) in the hydrogenbonding energy calculation, leads to better potential energy sur-faces of carbohydrates.1 Thus, the 6-311�G** basis set is chosenfor our work. Ten conformations are reported to represent trueminima for 1,2-ethanediol.27 For the torsional parameter fitting,further rotamers are generated. For the conformations with aO–C–C–O torsion (�) gauche and trans, rotamers in 30° incre-ments of the C–C–O–H torsional angle �1 are generated, whereasthe angle �2 is fixed at 180° (Fig. 2).

For hexopyranose, the many conformations are available fromthe work of Damm et al.,9 which are obtained via full geometryoptimizations using RHF theory and the 6-31G* basis set. TheHF-6-31G* level of theory is known to be adequate for glucoseconformations and can only be improved at an unattainable com-

putational expense considering the number of conformationsused.28 Our additional electronic structure calculations for derivingfurther hexopyranose conformations are therefore also performedat the RHF/6-31G* level, which has been used previously fordeveloping torsional parameters.29

Force Field Studies

The OPLS–AA potential energy functions and parameters areused9 with the exception of the torsional parameters, which arenewly derived, and the additional scaling factors used. The 1,5-electrostatic interactions are reduced for 1,2-ethanediol and forhexopyranoses by a factor 1.25 and 1.26, respectively. In addition,for hexopyranoses a scale factor equal to 1.22 is applied betweenthe 1,6-interacting atoms of the hydroxymethylene and the vicinalhydroxyl groups (Fig. 3). This scaling factor is necessary to restorethe balance with the 1,5-interactions.

Molecular mechanics calculations are performed with theGROMOS96 package30 that was adapted to reduce the 1,4-, 1,5-,and 1,6-electrostatic interactions. For geometry optimizations inGROMOS96, the conjugate-gradient algorithm is used with aconvergence criterion of 1 � 10�5 kJ/mol. The POTENT pro-gram31 is modified in order to provide the molecular topology filewith the OPLS–AA parameters for the GROMOS96 program. Inaddition to the standard OPLS–AA parameter data file, onlyatomic coordinates and OPLS atom types are required for the inputfile.

The following conditions are used for each simulation. Eachsystem consists of a single �-D-hexopyranose surrounded by waterin a cubic box subject to periodic boundary conditions to eliminateedge effects. For water the TIP3P model32 is used. The shortestdistance between the hexopyranose and the wall of the box isinitially 1.2 nm, where the number of water molecules varied from580 to 600, depending on the hexopyranose molecule and theinitial conformation. The simulations are performed at 1-atm pres-sure and 300 K by weak coupling33 to an external bath using thecoupling constants of 0.1 ps for the temperature and 0.5 ps for thepressure coupling. A cutoff radius of 9 Å for nonbonded interac-

Figure 2. Dihedral angle definition and partial charges (in e) used inthe force field calculations for the 1,2-ethanediol.

Figure 3. Pairs of atoms describing 1,6- and 1,5-interactions forwhich additional scaling factors are applied in the OPLS–AA–SEIforce field. For the 1,5 pairs, an example of the application of thescaling factor is given for one of the 1,5 pairs of atoms for hexopyr-anose (1) and glycol (2).

1418 Kony et al. • Vol. 23, No. 15 • Journal of Computational Chemistry

tions is used and a nonbonded pair list is updated every 5 MDsteps. After a minimization of the entire system, a 100-ps MDsimulation is performed with restraining the solute degrees offreedom to relax the surrounding solvent molecule, and to attain awell solvated equilibrium system. Following this, the samplingperiod or analysis period is performed and configurations arestored every 0.5 ps. Averages for 3JHH coupling constants arecalculated using a generalized Karplus equation:34

3JH,H � 13.22 cos2�� 0.99 cos��

� xi�0.87 � 2.46 cos2��i��19.9�xi�� .

In this equation � denotes the proton–proton torsion, �i stands for�1 or �1 according to the orientation of the substituent withrespect to its geminal proton. The factors of electronegativity (xi)are set 1.3 (O5 and O6) and 0.4 (C4).

Mean values for torsional angles of the hydroxymethylenegroup are determined according to the following procedure. Aconformation is considered g� if the torsion value is between 0 and120 degrees, t if the value is between 120 and 240 degrees, g� ifthe value is between 240 and 360 degrees.

Torsional Parameter Optimization

The FITGR program (a GROMOS adapted version of FITPARprogram35) is used to derive the torsional parameters. The heart ofthe FITGR routine is identical to the FITPAR routine. A differencefunction between the ab initio and molecular mechanics energies isconstructed among a set of structures and then minimized bytorsional parameters variation using the combination of a simplexand Fletcher–Powell algorithm. In contrast to FITPAR, FITGRreads the GROMOS topology and the two GROMOS geometryoptimization output files containing the atomic coordinates andpotential energy. The introduction of the new scale factor for the1,5- and 1,6-electrostatic interaction changes the nonbonded in-tramolecular potential. Following the procedure described previ-ously9 the set of torsional parameters optimized for the OPLS–AAforce field is adjusted. This set of torsional parameters is aug-mented by additional types (see below).

Results and Discussion

1,2-Ethanediol

In the following section we discuss the development of the OPLS–AA–SEI (OPLS–AA Scaling Electrostatic Interaction) force fieldand compare the gas phase energetics obtained from the ab initioand force field calculations using 1,2-ethanediol. In Table 1 therelative energies and the torsional angles (�, �1, �2 see Fig. 2)obtained for the 10 possible minima and the calculated rotamersare given. The relative energies obtained for the 10 minima at theB3LYP/6-311�G** level of theory are very close to the MP2energies obtained by Cramer and Truhlar,27 which confirms thequality of the additional rotamers.

The OPLS–AA and newly optimized OPLS–AA–SEI torsionparameters are given in Table 2. The torsional parameters describ-

ing the O–C–C–O torsion with a single V1 term did not optimallydescribe the energetics of 1,2-ethanediol with the OPLS–AA–SEIelectrostatic model. Thus, a set of three Fourier coefficients hasbeen used in the fitting.

The relative energies for the 1,2-ethanediol conformers androtamers are calculated using the standard OPLS–AA parameters,the OPLS–AA–SEI parameters and at ab initio level. The resultsare given in Table 1 and depicted in the rotational profile of Figure4. The RMSD between the ab initio and the force field calculatedrelative energies for all conformers is 0.07 and 0.51 kcal/mol forthe OPLS–AA–SEI and the standard OPLS–AA, respectively. Therange of energies spanned by the conformers is ca. 5.5 kcal/mol forthe ab initio and the OPLS–AA–SEI models and about 10 kcal/molfor the standard OPLS–AA. The energy of the intramolecularhydrogen bond between the two hydroxyls is evaluated by theenergy difference between the tG�g� and tG�t conformers (no-tation explained in ref. 27). A large deviation between the ab initioand OPLS–AA calculations is found for the relative energies ofthese two conformers, as shown in Figure 1. In contrast to theOPLS–AA force field, the OPLS–AA–SEI force field correctlyreproduces the ab initio results for these two structures (Table 1).The relative energy between a trans and a gauche conformation ofa C–C–O–H dihedral angle, presented by the structures tG�g� andg�G�g�, does not involve creating or breaking a hydrogen bond.The OPLS–AA–SEI closely reproduces the ab initio energy forthese two structures and the energy difference of 0.5 kcal/mol(0.30 kcal/mol for the OPLS–AA) between them. Structures tG�tand tTt allow us to compare the reproduction of the G�,T relativeenergies of the ab initio and DFT calculations (0.6 kcal/mol and0.9 kcal/mol, respectively) by the two force fields. OPLS–AA–SEIperforms well with a relative energy of 1.25 kcal/mol in compar-ison to OPLS–AA, which gives a relative energy for the tG�tconformation of almost 8 kcal/mol.

The energy profiles for the rotation around the C–C–O–Htorsion calculated at the ab initio, OPLS–AA and OPLS–AA–SEIlevel are presented in Figure 4 for the G� and T conformers. TheOPLS–AA–SEI force field calculated the g� and g� minimashifted by 30° with respect to the ab initio calculated values for theT conformer. Besides this deviation, the agreement between thequantum mechanics results and the OPLS–AA–SEI results is verygood. The largest deviations are obtained for the OPLS–AA forcefield, which yields a too large barrier for the two profiles. Inparticular, for the rotational profile in which the O–C–C–O dihe-dral is arranged gauche, the OPLS–AA force field deviates fromthe ab initio calculated relative energy by more than 4 kcal/mol.This indicates that the additional scaling factor dramatically im-prove the gas phase conformational energetics for 1,2-ethanedioland that applying this scaling factor will also improve the confor-mational energetics for carbohydrates.

Hexopyranoses

Torsional Parameter Optimization

The torsional parameters assigned to hexopyranose structures aregiven in Table 3. The “identical types” are kept fixed duringtorsional parameter optimization. As in the standard OPLS versionfor carbohydrates, these parameters are taken from OPLS–AA


values for alkanes, alcohols and ethers17 where scaling the 1,5-electrostatic interactions does not require a parameter refinement.The “new type” are those optimized for the OPLS–AA–SEI forcefield. For the OH–C–C–OH and C–C–O–H torsion the same ana-lytical form as for 1,2-ethanediol is taken for the hexopyranoses.However, it turns out that the 1,2-ethanediol Fourier coefficientvalues can be further improved for hexopyranose and they are

therefore reoptimized. The three sets of Fourier coefficients areoptimized for the O–C–O–(H, C) torsional types. In contrast to theOH–C–C–OH type, we find during torsional optimization that asingle V1 term is sufficient for the OS–C–C–OH torsion. TheOPLS–AA–SEI force field has three C–C–C–O parameters sets:C–C–C–OH for dihedral angle to the hydroxyl oxygen, C–C–C–OSfor the dihedral angle to the ether oxygen, and C–C–C–OS_ace that

Table 1. Relative Energies (kcal/mol) of the Glycol Conformers, Calculated at Different Levels of Theory,Together with the Results of the OPLS–AA–SEI and OPLS–AA Force Fields.

GLYCOL conformersa B3LYPb MP2c OPLS–AAd OPLS–AA–SEIe �1(°)f �(°)f �2(°)f

g�G�g� 1.18 1.20 1.47 1.28 277.7 60.8 277.5g�G�g� 2.96 3.22 4.02 3.14 45.7 53.5 45.9g�G�g� 0.49 0.31 0.30 0.50 75.1 58.1 314.7g�Tg� 2.69 2.99 2.88 3.75 65.9 176.6 66.0g�Tg� 2.99 2.80 1.81 2.63 69.7 179.9 290.4tG�g� 3.76 3.81 8.16 4.78 183.9 66.2 56.5tG�g� 0.00g 0.00h 0.00 0.00 193.4 61.7 306.6tG�t 3.54 3.48 7.87 3.80 180.0 60.0 180.0tTg� 2.79 2.91 2.31 2.98 186.5 180.2 70.8tTt 2.62 2.85 1.79 2.55 180.0 180.0 180.0transi 5.16 — 4.65 5.57 0.0j 180.0 180.0j

transi 4.13 — 3.69 4.68 30.0j 182.4 180.0j

transi 2.90 — 2.43 3.34 60.0j 180.1 180.0j

transi 3.00 — 2.65 3.06 90.0j 177.6 180.0j

transi 3.29 — 3.18 3.30 120.0j 176.2 180.0j

transi 2.92 — 2.46 2.92 150.0j 176.5 180.0j

transi 2.62 — 1.79 2.55 180.0j 180.0 180.0j

gauchei 3.23 — 4.18 3.61 0.0j 54.7 180.0j

gauchei 3.97 — 7.15 4.72 30.0j 62.7 180.0j

gauchei 3.78 — 8.28 4.25 60.0j 66.3 180.0j

gauchei 4.30 — 9.61 4.58 90.0j 69.0 180.0j

gauchei 4.75 — 10.34 4.90 120.0j 71.0 180.0j

gauchei 4.26 — 9.32 4.28 150.0j 72.4 180.0j

gauchei 3.54 — 8.07 3.53 180.0j 74.5 180.0j

gauchei 3.38 — 7.76 3.26 210.0j 75.6 180.0j

gauchei 3.00 — 6.87 2.60 240.0j 74.1 180.0j

gauchei 1.50 — 4.07 1.02 270.0j 70.0 180.0j

gauchei 0.17 — 0.99 0.02 300.0j 63.3 180.0j

gauchei 0.91 — 0.56 1.13 330.0j 55.5 180.0j

RMSDk

0.51 0.07

aThe label for each conformation indicates the �1, �, �2, dihedral angle. t (or T) means trans, g� (or G�) meansgauche� and g� means a gauche� conformation.bB3LYP/6-311 � G** relative energies in kcal/mol.cMP2/cc-pVTZ//MP2/cc-pVTZ relative energies in kcal/mol (ref. 27).dRelative energies from the OPLS–AA force field in kcal/mol.eRelative energies from the OPLS–AA force field in kcal/mol with a torsional parameter set optimized using a scalefactor for the 1,5 electrostatic interactions equal to 1.25.fB3LYP/6-311�G** optimized geometry.gEnergy � �230.3295503 au.hEnergy � �229.86044 au (ref. 27).iConformation is shown in rotational profile of Figure 4.jFixed dihedral angle.kRMSD for the energy difference between the B3LYP/6-311�G** and the force field calculated relative energies of thecorresponding column.


relates to the dihedral angle between the C3 ring carbon and theacetal group positioned on the C1 ring carbon. As for the uniqueC–C–C–O type of OPLS–AA, a single V1 term is sufficient for theC–C–C–OH. In contrast, three terms are more suitable for theC–C–C–OS torsion type. To correctly reproduce the methyl-hex-opyranoside relative energies, it is necessary to add the newC–C–C–OS_ace type. “Ace” means acetal and indicates the posi-tion of this dihedral in the molecule.

Comparison of Relative Energies Obtained with the TwoOPLS–AA Force Fields and at Ab Initio Level of Theory

In the following the performance of the OPLS–AA and OPLS–AA–SEI force fields in reproducing ab initio calculated relativeenergies of five different hexopyranoses is compared. The 44hexopyranoses structures included in the OPLS–AA parameterdevelopment are evaluated.9 Their relative energies are given inTable 4. The root-mean-square deviation (RMSD) between theOPLS–AA–SEI (OPLS–AA) and the ab initio calculated relativeenergy is 0.61 (0.75) kcal/mol for all the 44 conformers. TheRMSD for the 33 hexopyranoses with a hydroxyl at C1 (1, 2, 3;Fig. 5) is 0.65 (0.83) kcal/mol and 0.57 (0.42) kcal/mol for the 11hexopyranosides with a methoxy group at C1 (4, 5; Fig. 5). Thesimilar RMSD obtained for the OPLS–AA–SEI and the OPLS–AAforce field indicates that the new scheme with the reduced elec-trostatic interactions fits the torsional parameter with the samequality only. This can be understood because the set of carbohy-drate conformations consists of low energy conformations only. Asthe comparison of the conformational energetics for glycol shows,especially the high energy conformations are better reproduced withthe new force field so that the RMSD obtained for the 44 low-energycarbohydrate conformations is not reflecting an improvement.

The largest discrepancy (3.8 kcal/mol) between the ab initioand the OPLS–AA force field calculated energies is obtained forconformation 2f (Fig. 1). As expected, the OPLS–AA–SEI forcefield considerably improves the reproduction the ab initio relativeenergy of 2f. This shows that the additional scaling factor between1–5 interacting atoms restores the balance between the 1–4 and1–5 electrostatic interactions. Consequently, the OPLS–AA–SEI isable to reproduce the energetics of all the hexopyranoses showingthis structural change describing the exo-anomeric effect.

The corresponding �-anomers are represented by the structures2g and 2h (Fig. 6). Both force fields yield a too high relativeenergy for these two structures with respect to the ab initio levelcalculations. However, the OPLS–AA–SEI (OPLS–AA) forcefield gives a larger deviation for both structures 2g and 2h being1.5 (0.61) kcal/mol and 1.2 (0.95) kcal/mol.

Table 2. Sets of Torsional Angle Parameters for Glycol for the OPLS–AA Force Field and for theOPLS–AA Force Field using a 1,5 Scale between Electrostatics Interactions Corresponding to thePotential Energy Function.a

Etorsion � �i

V1i

2�1 � cos�� f1� � �

i

V2i

2�1 � cos�2� � f2� � �

i

V3i

2�1 � cos�3� � f3�

O—C—C—O C—C—O—H

V1b V2

b V3b V1

b V2b V3

b

OPLS–AA 9.508 0.000 0.000 �0.356 �0.174 0.492OPLS–AA–SEIc 4.780 �3.593 �0.887 �0.004 �0.629 0.035

a� is the dihedral angle, and f1, f2, f3 are all zero.bConstants are given in kcal/mol. The HCOH, HCCO, HCCH parameters are not optimized and stay identical to thestandard OPLS–AA values (ref. 9).cThe scale factor for the 1,5 electrostatic interactions is equal to 1.25.

Figure 4. Profiles for rotation around the C–C–O–H torsion in theT-(a) and G�-(b) 1,2-ethanediol conformation calculated ab initio atB3LYP/6-311�G** level and with the OPLS–AA–SEI and OPL-S–AA force fields.


An estimate of the energy difference between the conformerswith which the anomeric effect is described can be deduced fromthe energy difference between structure 1c and its correspondinganomer 1j. The ab initio (1.17 kcal/mol) and OPLS–AA (1.22kcal/mol) calculated energy differences are in a good agreement,whereas the OPLS–AA–SEI calculated energy difference is toohigh (1.94 kcal/mol). Finally, the relative energy of methyl-�-manno-pyranoside 5c is obtained too low by the OPLS–AA–SEIforce field by about 1.4 kcal/mol. This large discrepancy leads toa slightly larger value for the RMSD of the 11 methyl-hexopyr-anoses in comparison to the one derived with the OPLS–AA forcefield.

These results show that despite the fact that the OPLS–AA–SEIforce field considerably improves the largest discrepancies of theOPLS–AA force field, it does not reproduce the relative energy ofsome carbohydrate characteristic structural features as accurate asthe OPLS–AA force field. However, these few discrepancies couldturn out to be less important for the overall quality of the molecularmodel. This is illustrated in the following by comparing rotationalprofiles calculated with both force fields and at ab initio level.

Comparison of Rotational Profiles Obtained with theOPLS–AA and OPLS–AA–SEI Force Fields and at the Ab

Initio Level of Theory

Rotational profiles for the hydroxyl group at C1: the profiles forthe rotation around the C1–O1 bond are shown for the �- and

�-anomers of D-glucopyranose and D-mannopyranose (Fig. 7).They describe the energetics of the exoanomeric effect in hexopy-ranoses and show how the epimerization at C2, going from D-glucose to D-mannose, changes the energetics of the O–C–O–Hprofile. Overall, the OPLS–AA–SEI improves the description ofthis effect in comparison to the OPLS–AA force field. However,there are still discrepancies, which are important to consider infuture work. Parallel work done includes optimization of torsionalparameters using only the glucopyranose conformers for the fit-ting. The results show that in this case the parameters are able toreproduce the relative energy of rotamers and lowest energy con-formers with much better accuracy with respect to the ab initio.Therefore, considering other hexopyranoses, as the two anomers ofD-mannose in this case, into the fitting significantly increases thecomplexity of system and therefore leads to a lower quality of theO–C–O–H rotational profile calculated for D-glucose.

Rotational profiles for the hydroxymethylene group: the poten-tial energy profiles for rotation around the C5–C6 bond are exam-ined for the �-D-glucopyranose and the �-D-galactopyranose (Fig.8). The effect of the epimerization at C4, corresponding to thestructural difference of �-D-glucopyranose and �-D-galactopyr-anose, on the energetics of the different orientations of the hy-droxymethylene group is investigated.36 The hydrogen of thehydroxyl at C6 is held fixed at 180° with respect to the C5 atom sothat the possible intramolecular hydrogen bonds between the hy-droxymethylene group and the adjacent hydroxyl group and the

Table 3. Sets of Torsional Angle Parameters for Hexopyranoses for the OPLS–AA and OPLS–AA–SEIForce Fields Corresponding to the Potential Energy Function.a

Etorsion � �i

V1i

2�1 � cos�� f1� � �

i

V2i

2�1 � cos�2� � f2� � �

i

V3i

2�1 � cos�3� � f3�

OPLS–AA OPLS–AA–SEI

V1b V2

b V3b V1

b V2b V3

b

Identical typesC—C—C—C 1.740 �0.157 0.279 1.740 �0.157 0.279C—C—C—H 0.000 0.000 0.366 0.000 0.000 0.366H—C—O—C 0.000 0.000 0.760 0.000 0.000 0.760C—O—C—C 0.650 �0.250 0.670 0.650 �0.250 0.670H—C—C—O 0.000 0.000 0.468 0.000 0.000 0.468H—C—C—H 0.000 0.000 0.318 0.000 0.000 0.318H—C—O—H 0.000 0.000 0.450 0.000 0.000 0.450

Modified typesO—C—O—C �0.375 �1.358 0.004 �3.687 0.005 0.537OS—C—C—OH 4.319 0.000 0.000 1.593 0.000 0.000C—C—O—H 2.674 �2.883 1.026 0.205 �1.459 0.010OH—C—C—OH 9.066 0.000 0.000 8.519 �6.829 4.793O—C—O—H �1.257 �1.806 0.003 �1.673 �2.200 0.001C—C—C—OH �1.336 0.000c 0.000c �2.587 0.000 0.000C—C—C—OS �1.336 0.000c 0.000c �0.089 �0.729 0.870C—C—C—OS_ace �1.336 0.000c 0.000c 1.501 0.000 0.000

a� is the dihedral angle, and f1, f2, f3 the phase shifts. All phase shifts are zero.bConstants are given in kcal/mol.cC—C—C—O is unique in OPLS–AA.


Table 4. Relative Energies (kcal/mol) of Hexopyranoses at Ab Initio Level of Theory, and with the OPLS–AA and OPLS–AA–SEI Force Fields.

Conformersa HFb B3LYPc OPLS–AA–SEId OPLS–AAe O—C—O—X (°)f

1a �/cc/g�g� 0.86 0.57 0.44 1.13 63.3

1b �/cc/g�g� 0.94 0.58 0.68 0.94 61.7

1c �/cc/tg� 0.74 0.57 0.42 0.84 62.1

1d �/cl/g�g� 1.66 1.48 1.77 1.28 �164.9

1eg �/cl/tt 1.67 1.71 1.63 1.93 �164.7

1fh �/cl/tt 2.08 2.18 1.76 2.10 178.9i

1gh �/cl/tt 1.94 1.81 1.34 2.45 �152.2j

1hg �/cc/g�g� 1.86 1.31 2.58 2.43 �61.6

1i �/cc/g�g� 2.06 1.20 2.57 2.06 �62.9

1jg �/cc/tg� 1.91 1.42 2.36 2.09 �58.5

1k �/cc/tg� 2.99 2.34 2.20 2.64 38.7

2a �/cl/g�g� 0.00k 0.00l 0.00 0.00 �165.5

2b �/cc/g�g� 1.89 1.56 2.42 2.97 63.6

2c �/cc/g�g� 0.94 0.77 0.86 0.65 62.1

2d �/cc/tg� 0.97 1.55 0.73 0.94 62.7

2eg �/cc/tt 2.36 2.53 1.72 2.35 62.1

2fg �/cl/g�g� 2.29 2.10 2.43 6.14 69.1

2gg �/cc/g�g� 2.55 2.07 4.05 3.16 �61.1

2hg �/cc/tg� 2.42 2.77 3.60 3.37 �53.0

3a �/cl/g�g� 0.99 1.35 1.07 1.18 58.5

3bg �/cl/g�g� 2.93 2.94 3.90 2.94 57.2

3c �/cl/tt 1.44 1.96 1.20 1.32 58.1

3d �/cc/tg� 2.96 2.95 2.42 2.99 53.3

3eh �/cl/tt 2.61 3.18 2.37 2.70 30.0m

3fh �/cl/tt 1.45 1.95 1.43 1.46 60.0m

3gh �/cl/tt 2.69 2.70 1.26 1.50 90.0m

3h �/cc/g�g� 2.22 2.03 1.64 2.28 �48.7

3i �/cc/g�g� 2.32 1.81 1.13 0.93 �49.2

3j �/cc/tg� 1.86 1.72 1.20 1.21 �45.0

3k �/cl/g�g� 1.61 1.49 2.27 1.81 74.4

3l �/cl/tt 1.82 1.92 1.49 1.49 72.2

3mh �/cl/tt 2.12 2.36 1.56 1.70 60.0m

3nh �/cl/tt 2.49 2.29 2.54 2.51 90.0m

4a �/cc/g�g� 0.11 0.22 �0.11 0.32 67.7

4b �/cc/g�g� 0.00n 0.00o 0.00 0.00 64.9

4c �/cc/tg� 0.00 0.16 �0.12 0.06 67.0

4d �/cl/g�g� 2.90 3.05 3.14 2.95 72.1

4e �/cl/tt 2.94 3.33 3.19 3.44 71.8

4f �/cc/g�g� 1.23 1.11 1.79 2.04 �68.4

4g �/cc/g�g� 1.46 1.21 1.88 1.52 �68.8

4h �/cc/tg� 1.29 1.04 1.94 1.88 �66.7

5a �/cl/tt 0.99 1.97 1.03 0.58 66.3

5b �/cc/tg� 2.49 2.81 1.80 2.04 63.6

5c �/cc/tg� 1.61 1.93 0.18 1.66 �62.4

RMSDp

All 44 conformations 0.61 0.75Hexopyranoses 0.65 0.83Methyl-hexopyranosides 0.57 0.42

aThe label for each conformation indicates the anomer/the orientation of the hydrogen-bond network/the O—C5—C6—O and theC5—C6—O—H dihedral angles. t means trans, g� means gauche�, a g� means gauche� conformation. cc stands for counterclockwiseand cl for a clockwise hydrogen bond network.bRelative energies obtained at RHF/6-31G*//RHF/6-31G* in kcal/mol (ref. 9).cRelative energies obtained at B3LYP/6-311�G**//RHF/6-31G* in kcal/mol (ref. 9).dRelative energies obtained with the OPLS–AA–SEI in kcal/mol.eRelative energies obtained with the OPLS–AA in kcal/mol (ref. 9).fFor 1 � 3 X � H and for 4 and 5 X � CH3.gOptimization with a dihedral angle fixed at the torsional angle value of the corresponding HF ab initio-calculated structure.hConformation shown in rotational profile of Figure 7.iC2—C1—O—H angle fixed at 300°.jC2—C1—O—H angle fixed at 330°.kEnergy � �683.3352339 au (ref. 9).lEnergy � �687.4010763 au (ref. 9).mFixed dihedral angle.nEnergy � �622.3613721 au (ref. 9).oEnergy � �726.7106723 au (ref. 9).pRMSD for the energy difference between the RHF/6-31G* and the force field calculated relative energies of the corresponding column.

ring oxygen atom are avoided. The shape of these two profilescannot be explained in terms of classical effects (i.e., electrostaticand steric) alone. Stereoelectronic interactions favor the gaucheorientation of the O5–C5–C6–O6 unit.

The additional scaling factor used in the OPLS–AA–SEI forcefield significantly improves the reproduction of the ab initio-derived energies of certain conformations in the investigated ro-tational profiles. However, there are still large errors where theboth force fields show the same discrepancies. If the improvementin reproducing ab initio data also leads to better properties derivedin the liquid phase is tested in the following.

Liquid Simulation

The performance of the OPLS–AA–SEI and the OPLS–AA forcefield parameters sets in the liquid phase is evaluated in MDsimulations of �-D-glucose and �-D-galactose in explicit water.Rotation around the exocyclic C5–C6 bond of two hexopyranosesis expected to lead to three conformations, namely, g�, g� and t,which exist in an equilibrium (Fig. 9). The relative population ofthese conformations has been evaluated using 1H-NMR spectros-copy with which different ratios are obtained for D-glucose andD-galactose.37–39 Both intramolecular interactions and interactions

with the solvent determine the most populated structures. There-fore, reproducing the experimentally derived data will provide atest for the newly developed force field.

For hexopyranose the relative population is directly determinedfrom 10-ns MD simulations. The runs differ by the initial positionof the hydroxymethylene group. The g� and t starting conforma-tions are arbitrarily chosen for the �-D-glucose (Fig. 10), and theg� and t for the �-D-galactose (Fig. 11). Starting from differentconformations allows assessing whether the simulation time islong enough to obtain adequate sampling and converged values ofthe evaluated properties.

The rotation around the C5–C6 torsion for each run is shown asfunction time in Figures 10 and 11 and the relative populationratios are summarized together with the 3JHH coupling constants inTable 5. Not unexpectedly, the population ratios and the 3JHH

couplings lead to the same interpretations of the simulations. Theexperimental results show that �-D-glucose conformers are distrib-

Figure 5. Selected structures of the hexopyranoses under investiga-tion. (1) D-glucopyranose, (2) D-galactopyranose, (3) D-mannopyr-anose, (4) D-methyl-glucopyranose, (5) D-methyl-mannopyranose.

Figure 6. The two conformations of �-D-galactose used in the tor-sional parameter fitting. The hydroxymethylene group present a g�

(2g) and a t (2h) orientation.

Figure 7. Profiles for rotation around the C1–O1 bond in �- (a), �-(b), D-glucose and �- (c), �- (d), D-mannose calculated ab initio atHF/6-31G* level and with the OPLS–AA–SEI and OPLS–AA forcefields.

Figure 8. Profiles for rotation around the C5–C6 bond in �-D-glucose(a) and �-D-galactose (b) calculated ab initio at HF/6-31G* level andwith the OPLS–AA–SEI and OPLS–AA force fields.


uted as g�:g�:t � 56:44:0. The ratio obtained from the OPLS–AA–SEI for the �-D-glucose is in qualitative accordance with theexperimental results. The g� and g� species predominate, andthere is a negligible amount of the t conformation (69:27:4). Thesimulations carried out with a g� and t starting orientation of the

exo-cyclic hydroxymethylene group provide the same conforma-tional ratio (Table 5). The two simulations a and b using theOPLS–AA force field do not show the same ratio for the �-D-glucose. Starting from the g� conformer, the hydroxymethylenegroup prefers the g� orientation, while the g� and t conformersappear with equally low probability. Starting with the t conformer,the hydroxymethylene group is distributed as g�:g�:t � 45:51:4.After 10ns the conformational behavior of the hydroxymethylenegroup is still different in simulations a and b. Therefore, longersimulations would be required for obtaining a converged relativepopulation for the OPLS–AA force field. This indicates that theconformational space is less efficiently sampled using the OPL-S–AA force field.

From the measured J-couplings it is known that the �-D-galactose conformers are distributed as g�:g�:t � 17:63:20. TheOPLS–AA–SEI results present two distributions for simulations aand b (Fig. 11). Starting from the g� conformer (simulation a), thehydroxymethylene group is distributed as g�:g�:t � 9:53:38.Simulation a predicts the correct order of the conformer popula-tions with a maximum of 15% deviating from the experimentalvalues. Starting with the t conformer (simulation b), the hydroxy-methylene group is distributed as g�:g�:t � 4:35:61. This distri-bution of populations is different from simulation a but convergestowards the behavior of a towards the end (8–10 ns, 16:50:34).This indicates that there are still sampling problems for the OPLS–AA–SEI force field or that the 10ns simulation time is not longenough for obtaining a converged population ratio.

The OPLS–AA calculations present similar statistical resultsfor simulation a and b (Fig. 11). The predominance of the g�

conformer over the t conformer is well established by this force

Figure 9. The three minima of the hydroxymethylene groups, g�, g�

and t, of �-D-glucose and �-D-galactose, the two hexopyranose C4-epimers.

Figure 10. Time evolution of the dihedral angle O5–C5–C6–O6 of �-D-glucose in depen-dence of the indicated starting conformation.


field. The g� conformer has a too low population, which isconsistent with the OPLS–AA force field overestimating the gas-phase energy curves in the region of 240–360 for the galactose(Fig. 8). Further, differences between the conformations populated

in the liquid phase by the OPLS–AA–SEI and the OPLS–AA forcefield are found in the time evolution of the C1–C2–O2–H2 dihe-dral angle. The sampling problems mentioned above can be rec-ognized. The OPLS–AA force field obtains about one transition

Figure 11. Time evolution of the dihedral angle O5–C5–C6–O6 of �-D-galactose independence of the indicated starting conformation.

Table 5. J-Couplings and Populations of Hydroxymethylene Group Rotamers

J-coupling (Hz) Relative population (%)

JH5,H6R JH5,H6S g� g� t

�-D-glucoseH-NMR exp. 5.8 1.9 56 44 0OPLS–AA–SEIa

a:g� b 4.5 1.7 67 29 4b:tb 5.0 1.7 69 27 4

OPLS–AAc

a:g� b 10.0 4.6 12 77 11b:tb 6.9 2.8 45 51 4

�-D-galactoseH-NMR exp. 7.9 4.6 17 63 20OPLS–AA–SEIa

a:g� b 7.4 6.9 9 53 38b:tb 5.3 9.2 4 35 61

OPLS–AAc

a:g� b 7.1 7.7 2 52 46b:tb 8.5 6.4 3 64 33

aValues obtained from MD simulations using the OPLS–AA–SEI force field.bMD starting orientation of the hydroxymethylene group.cValues obtained from MD simulations using the OPLS–AA force field.


per nano second between different conformations, whereas theOPLS–AA–SEI obtains many. Considering the fact that the life-time of a hydrogen bond formed by a hexopyranose and a watermolecule is in average between 5 and 50 ps,40 one would expectrather more than just one rotation to occur. Visual inspection ofFigure 12 shows further that the g� conformation is populated themost by the OPLS–AA–SEI force field whereas the OPLS–AAforce field populates more g� conformations.

The gas phase rotational profile for the C1–C2–O2–H2 torsionis shown in Figure 13. The OPLS–AA force field obtains an energy

for the g� conformation, which is about 4 kcal/mol higher than theab initio calculations. This large discrepancy can be understood,because the geometries compared in this rotational profile differ infragments of 1,2-ethandiol, for which already such a large discrep-ancy between the ab initio and the OPLS–AA was found (Fig. 1).The improvement obtained by the OPLS–AA–SEI force field todescribe the gas phase energetics of 1,2-ethanediol is thereforedirectly reflected in this rotational profile. The relative energy forthe g� conformation calculated by the OPLS–AA–SEI force fieldis closer to the one calculated at the ab initio level of theory. Thelarge difference in the gas phase energy of the g� conformationsobtained for the two force fields leads to the different populationsof the conformations observed in the liquid phase. Unfortunately,there are no experimental data with which the most populatedconformation originating from different orientations of the C1–C2–O2–H2 angle could be identified.

Due to the mean field approximation used for deriving thenonbonded interactions of the OPLS–AA force field, the strengthof the intramolecular hydrogen bond formed in 1,2-ethanediol isexaggerated, and consequently, the conformations without such ahydrogen bond are found too high in energy (Fig. 1). Theseconformations without an intramolecular hydrogen bond form insolution more hydrogen bonds with the solvent than the confor-mation with an intramolecular hydrogen bond. Because, in com-parison to their gas phase interaction energy, the hydrogen bondsformed with the solvent are also exaggerated,3 the gas phaserelative energy of the conformations without an intramolecularhydrogen bond should, therefore, be higher than the ones derivedat ab initio level of theory. In this way, a proper balance betweenthe intra- and the intermolecular interactions is obtained in simu-lations using explicit solvent. It is, however, unclear how muchhigher in energy the conformations without an intramolecular

Figure 12. Time evolution of the dihedral angle C1–C2–O2–H2 of �-D-glucose andstarting conformation of the simulation.

Figure 13. Rotational profiles around the C2–O2 torsion in �-D-glucose calculated ab initio at HF/6-31G* level and with the OPLS–AA–SEI and OPLS–AA force fields.


hydrogen bond have to be relative to the lowest energy conforma-tions in the gas phase. This is a general problem of the parame-terization concept of pair-wise additive force fields, which makesit impossible to derive the torsional parameters systematically.

Opposite to this concept, the OPLS–AA–SEI parameter setdoes reproduce the ab initio-derived gas phase relative energy of1,2-ethandiol conformations without an intramolecular hydrogenbond. In this way, lower barriers for rotation are obtained forhexopyranoses and, therefore, far more transitions between differ-ent orientations of the C1–C2–O2–H2 angle are observed than inthe simulations conducted with the OPLS–AA force field (Fig. 12).The OPLS–AA–SEI force field therefore describes the conforma-tional behavior of a hexopyranose in aqueous solution in a morerealistic way than the OPLS–AA force field. Because the newscaling factors are applied within a hexopyranose only, and be-cause Vishnyakov et al.21 found that OPLS–AA describes theconformational space of a disaccharide in aqueous solution verywell, the OPLS–AA–SEI can be used to study polysaccharides insolution.

The application of an additional 1,5-scaling factor makes itnecessary to also add a 1,6-scaling factor to be able to fit thetorsional parameters. Trials to fit the torsional parameters withoutan additional 1,6-scaling factor and excluding the hexopyranoseconformations with an exocyclic hydroxymethylene group actingas hydrogen bond donor or acceptor have not been successful. Asoutline above, such a fitting procedure would be more compatiblewith the mean-field approximation applied in pair-wise additiveforce fields than applying the additional 1,6-scaling factor.

Conclusion

The OPLS–AA force field for carbohydrates is modified by ap-plying additional scaling factors for the electrostatic interactions ofthe 1,5- and some special 1,6-interactions and by adjusting thetorsional parameters. This new scheme for the electrostatic in-tramolecular interaction has considerably improved the force fieldreproducing the ab initio calculated relative energies of 1,2-ethanediol and the three hexopyranoses, glucose, mannose, andgalactose. For the new force field a similar RMSD between the abinitio calculated and the force field calculated relative energies isobtained for the 44 carbrohydrate conformers used for the param-eterization. However, it considerably reduces the largest deviationbetween the ab initio results and OPLS–AA force field, which areobserved when complete rotational profiles are compared. Thebarriers in such profiles represent conformations with broken in-tramolecular hydrogen bonds and are populated in aqueous solu-tion forming hydrogen bonds with the solvent. This indicates thatthe balance between strength of intra- and intermolecular interac-tions is shifted increasing the strength of intermolecular interactionenergies.

In the OPLS–AA force field, scaling of the 1,4-electrostaticinteractions by a factor of 2, causes an imbalance which is thesource of the largest deviation from the ab initio results. Adding1,5-scaling factors successfully restores this balance in hexopyr-anoses and, by scaling the excessive electrostatic contribution tothe total intramolecular energy, improves the conformational en-ergetics for 1,2-ethanediol dramatically. However, the addition of

a scaling factor for 1,5-interactions makes it necessary to add a1,6-scaling factor for particular interactions. Only with this 1,6-scaling factor it is possible to restore the required balance of theelectrostatic interactions to optimize the torsional parameters forcertain hexopyranose conformations. This limits the approachtaken in this work to improve a pair-wise additive force field to themolecular building block closed in itself, such as the one ofhexopyranoses. However, those molecular building blocks can becombined with each other, which leads in this case to polysaccha-rides. If the 1,5- and the 1,6-interactions between building blockshad to be scaled is currently being investigated by comparing thecomputationally determined conformational with experimentallyderived ratios.

The solvation effect on the conformational equilibria is inves-tigated by long time scale MD simulations on �-D-glucose and�-D-galactose. This tests if the gas phase energetics is reasonableand if the strength of the intramolecular interactions is in balancewith the strength of the intermolecular interactions. The populationratio of the conformations originating by rotation around theC5–C6 is directly determined for �-D-glucose and �-D-galactosefrom MD simulations. The simulations performed with the OPLS–AA–SEI accurately reproduce the glucose experimental results,whereas the simulations performed with the OPLS–AA force fieldsuffer from sampling problems. Nevertheless, results obtained for�-D-galactose indicate that there are still problems for the OPLS–AA–SEI force field or that the simulation time is not long enoughto obtain converged population ratios. In comparison to the OPL-S–AA force field, the new scheme obtains barriers for rotation ofhydroxyl groups, which are generally closer to the ones determinedat ab initio level, which leads to a higher hydroxyl transitionfrequency and better solvation in aqueous solution.

The structural features of carbohydrates, and of 1,2-ethanediolclearly demonstrate the limits of what can be handled with pair-wise additive force fields. The problems encountered indicate thata general improvement of the current molecular model can only beachieved by replacing the mean-field approximation used to de-scribe the polarized liquid state by an explicit treatment as done inpolarizable force fields.41 For the parameter development of po-larizable force fields it will be a good benchmark to test how wellcarbohydrates can be treated. Although proteins and peptides areof larger general interest, they do not challenge the force field asmuch as the structural features of carbohydrates do.

Acknowledgments

Gratitude is expressed to Dr. S. Telfer for helping to prepare themanuscript and Dr. P. Boulet for his help in conducting the abinitio calculations.

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