Comparison of Different Force Fields for the Study of Disaccharides

Carbohydrate Research 344 (2009) 2217–2228

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Carbohydrate Research

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Comparison of different force ﬁelds for the study of disaccharides

Carlos A. Stortz a,*, Glenn P. Johnson b, Alfred D. French b, Gábor I. Csonka c a Departamento de Química Orgánica-CIHIDECAR, FCEyN-Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina b Southern Regional Research Center, U.S. Department of Agriculture, 1100 Robert E. Lee Blvd., New Orleans, LA 70124, USA c Department of Inorganic and Analytical Chemistry, Budapest University of Technology, Szent Gellért tér 4, Budapest H-1521, Hungary article info abstract

Article history: Eighteen empirical force fields and the semi-empirical quantum method PM3CARB-1 were compared for Received 26 May 2009 studying b-cellobiose, a-maltose, and a-galabiose [a-D-Galp-(1?4)-a-D-Galp]. For each disaccharide, the Received in revised form 13 August 2009 energies of 54 conformers with differing hydroxymethyl, hydroxyl, and glycosidic linkage orientations Accepted 18 August 2009 were minimized by the different methods, some at two dielectric constants. By comparing these results Available online 22 August 2009 and the available crystal structure data and/or higher level density functional theory results, it was con- cluded that the newer parameterizations for force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) give Keywords: results that are reasonably similar to each other, whereas the older parameterizations for Amber, CHARMM Force field or OPLS were more divergent. However, MM3, an older force field, gave energy and geometry values com- Disaccharides Molecular mechanics parable to those of the newer parameterizations, but with less sensitivity to dielectric constant values. Cellobiose These systems worked better than MM2 variants, which were still acceptable. PM3CARB-1 also gave ade- Maltose quate results in terms of linkage and exocyclic torsion angles. GROMOS, GLYCAM06, and MM3 appear to Galabiose be the best choices, closely followed by MM4, CSFF, and OPLS-2005. With GLYCAM06 and to a lesser extent, CSFF, and OPLS-2005, a number of the conformers that were stable with MM3 changed to other forms. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction optimization (flexible residues) was just becoming available, but some early versions did not specifically treat the exoanomeric ef- Knowledge of the three-dimensional structures of disaccharides fect. is essential for understanding biological and physical functions. The anomeric effect is thought to arise from a combination of Determinations of the conformational preferences and variability electrostatic effects and rearrangement of the electronic structure, of disaccharides are useful not only for the disaccharides them- giving stabilization to certain conformations and not others. Such selves, but can often also apply to oligo- and polysaccharides hav- problems are the domain of electronic structure theory (quantum ing the same primary structure.1 This understanding can be aided mechanics or QM), which also has the capacity to describe all other by reliable molecular modeling. In the beginning, computerized molecular properties, including hydrogen bonding. In principle, disaccharide modeling relied on very simple models that varied quantum mechanics could answer most of the questions being the torsion angles of the glycosidic linkage but not the geometries asked in MM studies. Apparent success with the Hartree–Fock of the monosaccharide residues. Back then, structures were rated (HF) methods and modestly sized basis sets relies too much on as either ‘allowed’ or ‘disallowed’ based on interatomic distances. cancellation of errors, limiting the possibility of improvement. Later, potential energies were calculated for the rigid residue mod- Density functional theory (DFT) can provide reasonable results els based on van der Waals forces, twisting about bonds, and some- for saccharides,4 but at present it is also expensive in terms of com- times, emulation of hydrogen bonding. The HSEA2 and PFOS3 puter time and memory for large-scale calculations. Correlated potential energy functions for carbohydrates employed torsional wavefunction theory (e.g., MP2 or CCSD(T)) is even more expen- potentials that explicitly accounted for the exoanomeric effect sive. Although QM methods continue to improve, there is still a but still used rigid residues. This was a problem because the results great body of work for which MM methods are more suitable. from such studies depended very much on the particular choice of atomic coordinates used in the rigid residues.3 General-purpose molecular mechanics (MM) software that provided full geometry In MM software, the exoanomeric effect is supported in two ways. The more important is the recognition that the O–C–O–C torsión angle should have different parameters than the C–O–C–C torsión angle. Force fields do not meet that requirement if they base torsional energies on X–C–O–X, where X is any atom. * Corresponding author. Tel./fax: +54 11 4576 3346. Additionally, there are significant bond length variations associated with the E-mail address: [email protected] (C.A. Stortz). anomeric effect, and this has also been parameterized for some force fields.

MM methods now often employ parameters that allow the MM QM/MM method.31 The hybrid method was especially useful for software to mimic the results from QM studies on fragments of modeling sucrose. The conformational space of the desialyated Le- disaccharides. This allows MM to account for many factors, includ- wis X trisaccharide and its analogues was probed with HF and ing the exoanomeric effect. MM2* levels of theory.32 Momany and co-workers studied differ- Disaccharide analysis by modeling is a large-scale problem even ent conformations of maltose and cellobiose using DFT.33,34 Even if there is no worry about changes in the form of the pyranosyl though very large amounts of computer time were required, later rings. Disaccharide shapes are analyzed either by generating a QM studies yielded full maps of disaccharides, considered greater Ramachandran-like conformational map (contour map of energy numbers of conformers, or even undertook larger oligosaccha- vs / and w), or just by finding the energies of isolated minima. In rides.35–39 either case, such studies might explain experimental results. While Despite the improved MM methods, the chosen force field still it is often considered that the glycosidic torsion angles / and w influences the results. In 1998, Pérez et al. analyzed several mono- (Fig. 1) are the main variables of shape, there will be numerous sta- saccharides and a single disaccharide with different force fields ble conformers (‘multiple minima’)5 with different energies result- that were available then,40 focusing more on comparing the force ing from different combinations of the orientations of the primary fields to each other rather than on comparisons with the experi- and secondary hydroxyl groups. Preference for the given values of mental values. Since then, only a few comparisons of MM methods / and w will often depend on a particular combination of exocyclic have been published41 in spite of the new parameterizations and group orientations. For example, cellobiose has, in addition to / and functional variants for carbohydrates.24–29 Comparison of HF, hy- w, 10 exocyclic bonds about which rotation can occur. If each is al- brid DFT and MM2* results showed the difficulties in predicting lowed three staggered orientations, there would be 310 = 59,049 energies for carbohydrates with MM methods,42 attributed to their possible structures (for each /,w point). Many would not be stable, densely packed, highly polar functional groups, and the depen- but unless all are evaluated, it could be that the lowest energy value dence of conformational energies on stereoelectronic effects. will not have been found. In modeling studies, a frequent task is to MM2* gave good qualitative results for the lowest energy rotamers compare the depths of different energy wells on a /,w surface. In of monosaccharides, in spite of showing an energetically com- such work it is necessary to give a reasonably complete treatment pressed conformational space with incorrectly ordered rotamers of the exocyclic group orientations for each well to get an answer in the higher energy region. Other comparisons with several force that fully represents the particular computational method. fields have been made for QM results for glucose.43 Comparisons Flexible residue analysis3,6–8 of disaccharides started around have also been made with higher saccharides.32 1979 and by the late 1980s the first fully relaxed energy maps of Herein, we compare the performance of 18 different force fields numerous disaccharides had been constructed.9–11 Except for the or variants, some of them at two different dielectric constants, early Melberg and Rasmussen calculations,6–8,12 most were carried working with a set of 54 conformers each of b-cellobiose, a-malt- 13 out with Allinger’s MM2, by carbohydrate-specific variants like ose, and a-galabiose [a-D-Galp-(1?4)-a-D-Galp](Fig. 1) with vary- 3 14 MM2CARB, or with CHARMM and the carbohydrate parameters ing hydroxymethyl and hydroxyl group orientations. Although of Ha et al.15 Subsequently, MM3, an all-atom force field with up- PM3 and other semiempirical molecular orbital methods have graded parameterization for anomeric effects on torsional energies been shown to fail with carbohydrates,44 a variant parameterized and bond lengths as well as hydrogen bonding,16 was released and for carbohydrates (PM3CARB-145) has been issued. The perfor- used for many disaccharide studies.17–20 Earlier in the 1980s, many mance comparison with this semiempirical method is also new force fields were developed, some of them especially intended included. for molecular dynamics (MD) in general (like GROMOS21). Others In this comparison, we have not included the effects of explicit 22 18 targeted proteins or nucleic acids, such as Amber, CHARMM, and solvation. As some force fields have been parameterized to repro- OPLS.23 These force fields have been updated with parameteriza- duce the experimental data in solution, it might be considered tions that covered carbohydrates.24,25 Recently GLYCAM,26 a somewhat inappropriate to compare such force fields with those parameterization for carbohydrates of the Amber force field, was that did not include explicit water molecules during parameteriza- updated as a stand-alone, general-purpose force field useful for tion. We have proceeded on the assumption that, in principle, such molecules in addition to carbohydrates (GLYCAM06).27 Other spe- modifications to the force field should be minor (or not needed at cial parameterizations of force fields for carbohydrates have also all) so that the correct interpretation of the effect of explicit solvent appeared recently.28,29 QM methods have also been used directly. on the simulated system can be observed. Initially French et al. made adiabatic maps of disaccharide analogs 30 at the HF/6–31G* level, and then used them in a simple hybrid 2. Methods

2.1. Force ﬁelds

Molecular mechanics calculations were carried out: (a) using native MM3(92) (QCPE, Indiana University, USA), with the MM3(2000) values of the O–C–C–O and O–C–O–H torsional parameters, O–H hydrogen bonding parameters, and C–H electronegativity correction.46 Dielectric constants were kept at e = 1.5 and e =4.à The block diagonal minimizer was used, and the

à Allinger force fields use e = 1.5 for isolated molecules on the premise that since a molecule is present, there is not a vacuum. Other developers have used a value of e = 1.0. Dielectric constants intended for isolated molecules are suited for calculations to be compared with QM results and for molecule–molecule interactions, while we have found elevated e to be useful for the prediction of conformations in condensed phases (especially crystal structures) without explicit neighbors. Some force field Figure 1. The disaccharides studied in this work. The nomenclature of the torsion developers consider such predictions as inappropriate and discourage the use of angles is indicated for b-cellobiose. elevated dielectric constants. C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 2219 termination criterion was 100 times stricter than the default, that is, energies of hundreds of rotamers were calculated: those with the the calculation was stopped when the average movement was less lowest energy within each set of the /,w region and hydroxy- than 2 106 Å. Each resulting structure was confirmed as a mini- methyl rotamers were chosen. As no exhaustive search was made mum with a full matrix minimization and frequency calculation. for all 6561 combinations of OH group orientations, conformers (b) Using the program Tinker 4.2 (Washington University),47 with with lower energy could exist. However, it was not our purpose force fields MM2 and MM3 at e = 1.5 and e = 4. The final gradient here to determine the particular ideal conformers, but to only pro- was kept at 0.01 kcal mol1 Å1. (c) Using PCModel 9.2 (Serena Soft- vide a range of stable starting structures that can be tested with ware), for force field MMX at e = 4, using default termination condi- the different methods. In order to obtain those MM3-minimized tions. (d) Using Hyperchem 848 for the force fields MM+, Amber (3, structures, the input structures contained the following /,w an- 94 and 99), CHARMM (17, 22, and 27) and original OPLS, and with gles: for cellobiose, 75°, 123° (A region), and 88°, 163° (B re- the semiempirical method, PM3CARB-1.45 In all the Hyperchem gion); for maltose, 98°, 144° (A region), 68°, 168° (B region), and MM cases the dielectric constant was kept at its default value, and 95°, 75° (D region); for galabiose, 102°, 160° (A region) and 76°, the final gradient was set at 0.01 kcal mol1 Å1. (e) Using native 105° (B region). The starting geometry for the D region of maltose MM4,49,50 with dielectric constants of 1.5 and 4. The termination was chosen to be far from its final point, in order to avoid drifts to condition was average movement <2 106. This was 100 times the A region. The MM3 (e = 4) minimized structures were used as stricter than the default. (f) Using MacroModel51 with the OPLS- starting points for the calculations with other force fields and pro- 2005 force field52 and the Polak–Ribiere conjugate gradient mini- grams. In each case, the energies and geometries of the resulting, mizer and dielectric constants of 1 and 4.§ The termination condition optimized conformers were compared within themselves. Besides was a gradient <1.2 104 kcal mol1 Å1. This is 100 times stricter the A and B minima for cellobiose, a set of nine cellobiose ‘flipped’ than the default condition. (g) Using native Amber1053 with the GLY- conformers (i.e., those in the region around /,w =60°, 120° CAM0627 parameters, the limited-memory Broyden–Fletcher–Gold- (Fig. 2) was created. All nine combinations of hydroxymethyl ori- farb–Shanno quasi-Newton minimizer, and dielectric constants of entations were represented, with the secondary hydroxyl groups 1 and 4. We used the smallest available termination criterion, a gra- set in an anticlockwise (rr0) arrangement of hydrogen bonds.34,60 5 1 1 dient <1.0 10 kcal mol Å . This is 10 times stricter than the For these ‘flipped’ structures, the v6 were chosen to give the lowest 54 default. (h) Using the native CHARMM program and CSFF variant of energy using MM3 at e = 1.5. the force field with its default termination criteria and the adopted basis Newton–Raphson minimizer. (i) Using native Gromacs55 with 2.3. Indicators from the calculations the GROMOS96 force field,21,56 and both the 45a428 and the 53a657 parameter sets with the default termination criteria. As both give The following definitions4 of the relative energies were used practically the same results, only those of the 45a4 set (recom- DE ðconf ; conf Þ¼E ðconf ÞE ðconf Þð1Þ mended for carbohydrates) are included in this paper. model i ref model i model ref

is the relative energy of the ith conformer, confi compared to the en- 2.2. Nomenclature and starting geometries ergy of a reference conformer, confref using a given model chemistry (force field, program, and e). The torsion angle x is defined by the atoms O-5–C-5–C-6–O-6, DDE ðconf ; conf Þ primed for the non-reducing end. As usual, the rotamers are classi- model Amodel B i ref fied as gt (x 60°), tg (x 180°)orgg (x –60°). For the disac- ¼ DEmodel Aðconfi; confref ÞDEmodel Bðconfi; confref Þð2Þ charide, the orientation of the hydroxymethyl groups is is the relative energy difference of the ith conformer calculated with expressed with the non-reducing end first (e.g., gggt indicates a two different model chemistries. non-reducing end with gg orientation, and a reducing end with gt The model and reference conformer dependent mean absolute orientation). The glycosidic torsion angles / and w are defined by deviation (MAD) is defined as the atoms O-50–C-10–O-4–C-4 and C-10–O-4–C-4–C-5, respectively. The orientation of the hydroxyl hydrogen atoms is indicated by v , n MADmodel Amodel Bðconfref Þ defined by the atoms H-n–C-n–O-n–H(O)-n, whereas v is defined 6 1 Xn by the atoms C-5–C-6–O-6–H(O)-6, primed when appropriate ¼ jjDDE ðconf ; conf Þ ð3Þ n 1 model Amodel B i ref (Fig. 1). All starting structures had their pyranosyl rings in the most i¼1 4 stable, C1 conformation. The nomenclature for the regions of min- imal energy (A, B, and D) follows the conventions used previ- Note that within a given test set of conformers the MAD be- ously58,59 for the three disaccharides (Fig. 2). tween the two compared models (model A and model B) depends The 54 starting conformers for cellobiose and galabiose con- on the choice of the reference conformers. One way to eliminate sisted of 27 in the A region and 27 in the B region. Each set of 27 this problem is to compare the range of DDEmodel Amodel B(confi, corresponded to three combinations of OH orientations, combined confr) values of Eq. 2. The range of the relative difference was de- with each of the 9 combinations of both hydroxymethyl groups in fined as RRD = max DDE min DDE. The reference conformers gt, gg,ortg orientation. For maltose, which has three main regions for maltose and galabiose had the lowest energy with MM3 of minimum energy (A, B, and D, Fig. 2), only two combinations of (e = 4) along with the gtgg orientation, whereas for cellobiose the OH orientations were used for each combination of hydroxymethyl reference structure is gtgt. rotamers. The three conformers (two for maltose) were chosen after a preliminary study made with MM3 at e = 4, where the 3. Results and discussion

The 54 conformers of each of the three disaccharides (Fig. 1) § Whereas the results from dielectric 1 from CHARMM and Amber studies can be fairly compared with the dielectric 1.5 results from Allinger’s MMn calculations, were geometry-optimized with different methods (method = force studies based on a dielectric constant of 4 are not strictly comparable. In the case of field + dielectric constant + program). Table 1 shows the number of MMn, a dielectric constant of 4 corresponds to a reduction of the electrostatic conformers that remained in their original region of minimum en- energies by a factor of (1.5/4) or 0.375. For methods that assume a dielectric constant ergy, that retained their x angles (within ±60°), and that were not of 1 for isolated molecules, an increase to dielectric 4 reduces the interactions by a factor of 0.25. MM4 hydrogen bonding energies are based on both dipole–dipole identical to another conformer in the list. With the three disaccha- interactions and on an extra term that does not depend on the dielectric constant.50 rides, there were negligible differences in geometries and energies 2220 C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 in the results obtained with Tinker MM3 and the original MM3 Table 1 a program. Thus, only the results obtained with native MM3 are Number of conformers remaining after minimization with each method shown below. Method b-Cellobiose a-Maltose a-Galabiose ABA BDA B 3.1. b-Cellobiose MM3 (e =4) 27271818182727 MM3 (e = 1.5) 27 26b 17b 15b,c 16b,d 24b,c,d 26d There are numerous studies of the adiabatic map of b-cellobi- MMX (e =4) 27 24b 8d 18 18 27 27 ose.7,12,18,20,36,38,58 Two minima, very close to each other in energy, Tinker MM2 (e =4) 27 27 17b 11d 18 27 24d b d b d have similar / torsion angles but are displaced about 40° in the w Tinker MM2 (e = 1.5) 27 27 17 10 18 26 23 MM+ (e = 1.5) 27 24b 18 17d 18 27 27 torsion angle. These minima were designated as A and B.38,58 The MM4 (e =4) 27 26d 16b,d 17b 16d 26d 27 current survey, made with 27 A conformers and 27 B conformers MM4 (e = 1.5) 27 26d 14d 16b 15d 27 25d (Fig. 2) showed, at least with MM3, that every hydroxymethyl ori- Amber3 27 27 16d 18 18 27 27 entation can be stable. Table 1 shows that the 27 minima in the A Amber94 27 24b 11d 18 17d 27 27 e e region are quite stable regardless of force field, as only seven in- Amber99 27 27 13 18 17 27 27 GLYCAM06 (e =4) 27 11d 17d 9d 5d 13d 27 stances of departure from the original structure occurred with GLYCAM 06 (e =1) 27 6d 17b 8b,d 8d 24b,d 25b d d d d the MM methods. Besides, six A minima were unstable with CHARMM 19 27 8 2 18 17 27 14 d d PM3CARB-1. Conformers in the B region were also stable when CHARMM 22 27 27 18 0 2 27 27 e b,e d e e minimized by most force fields, but quite a few converted to the CHARMM 27 26 18 0 14 15 27 27 CSFF (e =4) 27 22d 18 4d 10d 22d 27 A region with GLYCAM06, CHARMM19 or OPLS-2005. Figure 3 shows CSFF (e =1) 22b,d 19b,d 17b 10b,d 11d 26d 22b,d the /,w regions for the A and B minima calculated with each force OPLS original 27 24b 14d 16d 15d 27 27 field. Table 2 compares the torsion angles of the remaining exocy- OPLS 05 (e =4) 27 14d 16d,e 18 15d 26d 27 b d b,d,e b,d d b b,d clic bonds (v20 , v30, v40, v60 , x0, v1, v2, v3, v6, and x), indicates OPLS 05 (e =1) 26 9 10 13 16 26 20 which of the 54 conformers is the global minimum within each cal- GROMOS (e =4)27271818182727 GROMOS (e =1) 27 27 17b 18 14d 27 26b culation, and gives the statistical comparison of the force fields PM3CARB-1 21b 18b,d 11b,d,e 9b,d,e 13d,e 20b 23b,d with the ‘reference models’. Figure 3 shows that the CHARMM vari- a The number of starting conformers for cellobiose and galabiose was 27 for each of ants give rather different /,w locations, especially CHARMM27. Allin- the A and B regions, and for maltose 18 in each of the A, B, and D regions. ger’s MM force fields all gave similar /,w locations, and Amber3 b The remaining conformers were lost due to: passage to other existing conformers minima are also close by. The newer force fields’ minima are closer in the same minimum energy region; c imaginary frequencies; d passage to another to those of the MMn force fields when working at e =4. minimum energy region; e rotation of one of the hydroxymethyl groups of more Keeping in mind that the packing effects can influence the /,w than 60°. position of crystalline disaccharides, especially in shallow minimum-energy regions, we are comparing the different results with our modeling calculations. The crystal structure of b-cellobiose61 provided an A-gtgt conformer as the global minimum was MM3 at shows /,w values of 76°, 132°, in the A region. MM2 and espe- e =4(Table 2). However, by most of the other methods, the most cially GROMOS (e = 1) give A minima closest to this value (Fig. 3), stable A-gtgt conformer had energies 0.121.45 kcal/mol above although MM3 and the newer force fields CSFF, OPLS-2005, and the global minimum. The only methods that gave higher energies GLYCAM06 (at e = 1) are also very close. Both hydroxymethyl were OPLS-2005, MM4, CSFF, and GLYCAM06 when working at groups in the crystal have the gt orientation. The only method that low dielectric constants, and CHARMM27 (29 kcal/mol). Many other

Figure 2. Molecular representations of the minima in each region for the three disaccharides. The geometries correspond to those of lowest energy using MM3 at e =4. C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 2221

Figure 3. Representation of the /,w areas calculated in the A and B regions with each method for b-cellobiose. Each ellipse is centered at the average /,w point obtained for each method and shows axis magnitudes given by the standard deviation. The ellipses are color-coded. Those with cross hatched lines were made at e = 4, whereas the solid or diagonal line ﬁllings correspond to vacuum calculations.

Table 2 For b-cellobiose, geometry of the global minimum (for MM3 at e =4,A gtgt), comparison of the geometries of the conformers minimized by each method with those obtained with MM3 (e = 4), mean absolute deviations (MADs), and range of relative differences (RRDs) against different reference models

Minimum Average difference of Most affected torsionals (average) vs MM3 (e = 4) vs MM3 (e = 1.5) vs Amber94 the 10 exocyclic torsionals (°) MAD RRD MAD RRD MAD RRD MM3 (e = 1.5) A, gttg 5.4 ± 3.0 Evenly distributed (3-8°) 0.93 5.37

MMX (e =4) B, gtgt 8.8 ± 11.3 v3 (30°); v1 (13°) 1.15 2.04

Tinker MM2 (e =4) B, gttg 10.0 ± 12.9 v1 (40°) 0.95 4.60

Tinker MM2 (e = 1.5) B, tgtg 10.9 ± 12.2 v1 (45°); v6 (10°) 1.30 5.44 0.81 2.77

MM+ (e = 1.5) B, gtgg 4.5 ± 5.3 v3 (13°) 1.38 2.87 1.08 5.35

MM4 (e =4) A, gtgg 10.7 ± 6.1 All but the x (v20 , v30 & v2, 16-17°) 0.74 3.62

MM4 (e = 1.5) B, gtgg 9.2 ± 5.7 v30 , v20 , v40 , v2 & v3 (11-15°) 1.58 6.63 1.07 3.42 Amber3 A, gtgg 4.6 ± 4.4 Evenly distributed (2-9°) 0.98 2.19 1.03 4.99 1.15 4.22

Amber94 A, gtgg 10.3 ± 13.8 v3 (30°); v40 (11°) 0.77 4.02 1.56 8.53

Amber99 A, gtgg 5.9 ± 6.4 v3 (13°); x0 (10°) 0.90 4.37 1.67 8.83 0.41 1.22

GLYCAM06 (e =4) A, gtgg 4.0 ± 5.1 v1 (15°) 0.35 1.70 0.61 2.68

GLYCAM06 (e =1) A, tgtg 8.2 ± 10.8 v1 (38°) 2.22 7.56 1.82 4.34 2.41 10.1

CHARMM 19 A, tgtg 11.8 ± 10.9 v3 (36°), v30 , v40 , v20 , v6, v60 (10-15°) 2.13 4.60 1.78 3.33 2.10 6.58 CHARMM 22 B, gttg 12.1 ± 6.6 Evenly distributed (8-16°) 1.79 4.23 1.43 5.28 2.20 7.61

CHARMM 27 B, gggt 8.2 ± 15.2 v3 (34°); x0 (11°) 2.75 5.50 2.73 10.4 2.81 6.68

CSFF (e =4) A, gggg 7.3 ± 5.1 x’, x & v3 (11°) 1.43 7.10 0.74 4.00 CSFF (e =1) B, gtgg 7.6 ± 17.7 x (18°), rest evenly distributed (3-9°) 4.20 10.9 3.79 11.5 4.38 12.6

OPLS original A, gtgg 10.7 ± 13.5 v3 (36°); v40 (12°) 0.85 4.23 1.60 8.15 0.40 1.68 OPLS 05 (e =4) A, tggt 3.6 ± 4.2 x (11°), rest evenly distributed (2-6°) 1.62 6.71 2.14 9.51

OPLS 05 (e =1) A, gttg 8.1 ± 6.1 v3, v2 & v40 (11-13°) 1.52 7.07 1.59 6.90 1.96 9.81

GROMOS (e =4) A, gtgg 4.3 ± 5.3 v3 (12°) 1.49 6.09 0.97 2.50

GROMOS (e =1) A, gttg 7.7 ± 6.4 v3 (20°), v40 (11°) 1.55 6.25 0.93 4.79 1.98 8.47

PM3CARB-1 A, gtgg 7.7 ± 8.9 v1, v3 & x (12-15°) 1.23 5.61 1.08 5.53 1.50 6.16

Units of MAD and RRD are kcal/mol.

diffraction studies have been carried out on related molecules, products appear in the A region (/ 75°, w –104° to 110°), as such as higher oligomers, derivatives with the hydroxyl groups gggt rotamers. The non-reducing end and central residue of cello- partly or totally substituted, and with solvates that incorporate triose undecaacetate are linked with bonds having / = 98°, water, MeOH, or EtOH.62 Most of the fully O-acetylated crystalline w = 143°, with O-6 atoms gggg, closer to the B region.63 Methyl 2222 C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 glycosides tend to appear in the B region (/ 90°, w 141° to Table 3 161°). Relative energies of the most stable conformer in the flipped region of b-cellobiose with respect to those in the normal region, determined by different methods Although most of the hydroxymethyl groups are gt, there are some (especially at the reducing end) appearing as gg. Only one DE (kcal/mol) Minimum 64 example of a tg hydroxymethyl group has been found in mole- DFT (from Ref. 34) –2.55 gggg cules related to cellulose despite the rotamer being found in native MM3 (e = 4) 3.41 (4.73)a gggg 65 cellulose. The appearance of crystalline forms in the A and B min- MM3 (e = 1.5) 0.00 (2.30)a gttg imum energy regions, and with gt, tg,orgg orientations suggests MMX (e = 4) 1.88 gtgt very low differences in energy among the conformations. Tinker MM2 (e = 4) 1.49 gttg Tinker MM2 (e = 1.5) 0.39 gttg Regarding the exocyclic groups (Table 2), the force fields closest MM+ (e = 1.5) 2.45 gtgt to MM3 (e = 4) are MM+, Amber3, Amber99, GROMOS, GLYCAM06, MM4 (e = 4) –0.92 gttg and OPLS-2005 at e = 4. The two main exocyclics that change are v1 MM4 (e = 1.5) –2.90 gttg and v3 (Table 2). Susceptible to the exoanomeric effect, v1 is about Amber3 1.43 gggg 50° in MM3 and most of the other force fields. However, MM2 and Amber94 2.78 gtgg Amber99 2.47 gggg GLYCAM lead it to a value up to 90°. The other major variability GLYCAM06 (e = 4) 0.77 gggg was for v3, especially in the B region. Some force fields (notably GLYCAM 06 (e = 1) –4.66 gggg the 19 and 27 versions of CHARMM, the 94 and 99 versions of Amber, CHARMM 19 2.15 tggg and MMX) force it close to 50°, whereas the other force fields place CHARMM 22 5.64 gttg H(O)-3 in a variety of orientations depending on the other hydroxyl CHARMM 27 3.52 gggg CSFF (e = 4) 1.80 gggg orientations. The behavior of the Amber variants with regard to v2 CSFF (e = 1) –1.51 gggg is noteworthy. Minimization yielded two conformers with exactly OPLS original 3.50 gtgt the same energy and the same absolute value of v2. However, the OPLS 05 (e = 4) –0.01 tgtg OPLS 05 (e = 1) –5.07 gggg sign of the v2 angle is different, even though all the remaining an- GROMOS (e = 4) 1.47 gtgg gles are identical. The H-bond interaction of H(O)-2 with O-3 or GROMOS (e = 1) –6.19 gggg with O-1 gives exactly the same total energy to the whole PM3CARB-1 –0.35 gggg molecule. The hydroxymethyl geometries of the most stable conformers are also indicated. Most force fields (Table 2) show the A region to have a lower en- a In parentheses, free energy. ergy than the B region. However, two CHARMM variants, the two MM2 variants, and CSFF and MM4 at low dielectric constant show the B region as predominant. The hydroxymethyl groups of the global minima are in gg, gt,ortg orientation, depending on the force dielectric constant, with a higher energy at e = 4. At the same time, field (Table 2). According to the MAD and RRD, the force field that MM3 at e = 1.5 gives equal energies for the most stable conformers shows the best energy coincidence (Table 2) with MM3 (e =4)is in each region (Table 3). PM3CARB-1 also predicts more stability GLYCAM06 (e = 4). The Amber variants and MM4 also show a good for the flipped conformer. The energy difference predicted by match. It is noteworthy that the Amber variants, although made at DFT is closer to that obtained by MM4, and also close to those pre- the default dielectric constant (e = 1), match better with the results dicted (in order) by CSFF, GLYCAM06, PM3CARB-1, OPLS-2005, of MM3 at e = 4 than with those made at e = 1.5. A similar effect MM3, MM2, and GROMOS. However, MM4 and OPLS-2005 show was found with CHARMM. Furthermore, Amber94 shows a good a disadvantageous feature: even at e = 4 a flipped conformer is match (Table 2) with GLYCAM06 (e = 4) but not with GLYCAM06 more stable than the ‘normal’ forms. Most of the newer force fields at e =1. show the same preferred conformer as DFT, gggg. On the other DFT studies of b-cellobiose showed34 that the global minimum hand, the values of the /,w angles found by DFT34 (after conversion corresponds to a conformer located within an unusual /,w region, from H-based angles to C/O based angles) shown in Figure 4 match still influenced by the exoanomeric effect but sterically not very excellently with those of MM3, GROMOS, and MM4 and are also in advantageous.20 This region, around /,w =60°, 120°, received dif- good agreement with the other new force fields at e = 1. While the ferent designations as ‘side-of-the-map’,20 ‘flipped’,34 or ‘folded’.36 location of the minima from the various force fields (except MM3) The original B3LYP/6-311++G(d,p) results34 were also confirmed by did not coincide exactly with the DFT results when working at e =4 less-expensive HF/6-31G(d) and B3LYP/6-31+G(d) calcula- (Fig. 4), most discrepancies are minor in terms of degrees. As ob- tions.36,38It has been explained that the great stability of this con- served with B3LYP/6-31+G(d) calculations, all the flipped conform- former, which does not correspond to any of the known crystalline ers fall into a smaller part of /,w space.66 forms, is due to an anti-clockwise arrangement of hydrogen bonds involving both sugar rings.60 Thus, it is expected that a force field 3.2. a-Maltose working at low dielectric constants with good parameterization of hydrogen bonding would also favor the flipped forms. French The adiabatic map of a-maltose has also been studied exten- and Johnson observed66 that the numerous flipped conformers all sively.6,10,17,20,58 Although it was also thought that only two min- fell into a smaller part of the /,w space than for the other regions, ima appear in the lower-energy region, an adjacent third something that might also occur with the MM force fields. minimum has been described. According to older MM3 calcula- Nine conformers of b-cellobiose in the flipped region (Fig. 2) tions58 minima A and B differ by about 30° in / and 25° in w, that with different arrangements of hydroxymethyl groups but the is, they are more separated in / than in w. Minimum A appeared to same anti-clockwise arrangement of the secondary hydroxyl have slightly lower energy. However, a third minimum (D), with groups were studied as above. Results are shown in Table 3, and higher energy has been found, occupying a region which is 20° in Figure 4 compares the location of the /,w angles with those of / and 35° in w from A, further away from B.58 The current work the DFT calculation.34 Table 3 shows that the older force fields was carried out with 18 minima each in the A, B, and D regions (Amber, CHARMM, MM2 variants, original OPLS) did not indicate (Fig. 2), including all nine staggered combinations of hydroxy- greater stability for the flipped conformers. On the other hand, methyl orientations. The closeness of the three minima allows the newer force fields MM4, GLYCAM06, CSFF, OPLS-2005, and many passages from one minimum energy region to another (Table GROMOS show one flipped conformer as the most stable at low 1). Thus, no method (besides MM3 and GROMOS at e = 4) was able C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 2223 to keep the original 54 conformers. CHARMM27 did not keep any A shifts of D and B conformers to the A region, whereas for Amber minimum conformers, and CHARMM19 kept only a few. In contrast, versions the A conformers shifted somewhere else. Figure 5 shows CHARMM22 kept all the A minimum conformers, the B conformers the distribution of /,w angles in each region: in the D region some shifted to A, and only two D conformers were stable. PM3CARB- methods give very wide ellipses, suggesting a great degree of /,w 1, Amber99, and CHARMM27 showed a tendency to shift tg conforma- variability depending upon hydroxyl and hydroxymethyl group tions to gt and gg rotamers. GLYCAM06 and CSFF showed many orientations. On the other hand, the A and B regions show less

Figure 4. Representation of the /,w areas calculated in the ‘ﬂipped’ region (see text) with each method for b-cellobiose. Each ellipse is centered in the average /,w point obtained for each method, and shows axis magnitudes given by the standard deviation. The ellipses are color-coded. Those with cross hatched lines were made at e =4, whereas the solid or diagonal line ﬁllings correspond to vacuum calculations. The black bordered-white ellipse corresponds to the DFT results of Strati et al.34 The arrows for CHARMM19 and CHARMM27 point to locations off the plot, centered at /,w = 34.9°, 111.4°, and 56.3°, 174.9°, respectively.

Figure 5. Representation of the /,w areas calculated in the A, B and D regions with each method for a-maltose. Each ellipse is centered in the average /,w point obtained for each method, and shows axes magnitudes given by the standard deviation. The ellipses are color-coded. Those with cross hatched lines were made at e = 4, whereas the solid or diagonal line fillings correspond to vacuum calculations. 2224 C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 variability when working with different methods. CHARMM27 again 100° at lower dielectric constants, and to even higher absolute val- gives /,w values distant from the average values. In the A and D re- ues (150°) with MM4. Amber and other force fields have a smaller gions the newer force fields (GROMOS, GLYCAM, OPLS-2005 and change of these v20 values, but also change other v values so the aver- CSFF) tend to form differentiated subregions at e = 1 and e =4.Ta- age is also high. Using MM3, almost all conformers have a v2 with ble 4 compares the torsion angles, shows which of the 54 conform- values of either 65° or 165°. They do not change very much with ers is the global minimum for each method, and gives the statistics other force fields (e.g., Allinger MMn variants or GLYCAM), but they for comparison of the force fields with the ‘reference models’. switch to values of 50–58° and 173–180°, respectively, with Am- 67 The crystal structure of a-maltose has /,w of 116°, 118°, ber94, Amber99, CHARMM27, or OPLS. For maltose, most force fields matching our D region /,w values determined using MM4 and is (Table 4) show some A and gtgg conformer as the preferred mini- not far from the minimum given by PM3CARB-1 (Fig. 5). These mum. Amber3 and CHARMM27 show the same gtgg rotamer as pre- two methods were the only ones to find the D region to have the ferred, but in the B region. Other CHARMM variants, Amber94 and lowest energy (Table 4). The crystal structures of the hydrates of OPLS-2005 at e = 4 also give a B minimum. Additionally, MM4 and b-maltose and its methyl glycoside also fall within the D region,68 PM3CARB-1 show a D minimum. It should be noted, however, right in the middle of the MM4 and PM3CARB-1 ovals (Fig. 5). For (Fig. 5) that these D minima are located closer to the A region than these three compounds, the hydroxymethyl rotamers were either those produced by other methods (with the exception of GROMOS gtgt or gtgg. On the other hand, acylated derivatives of b-malt- at e = 1). GLYCAM06 (e = 4) again shows the best coincidence in en- ose69,70 appear in the B region, with /,w values close to those of ergy (Table 4) with MM3 (e = 4). The Amber variants again show a MM4. Their hydroxymethyl groups appeared in various orienta- good match, but MM4 does not. tions, including tg for the non-reducing end.69 Finally, higher olig- Momany and co-workers have studied several conformers of a- omers and phenyl b-maltoside appear in the A region, and the maltose by DFT.35 From their supplementary material we were hydroxymethyl groups are gg or gt, depending on the compound.71 able to pick 3 conformers in the A region, 5 in the B region and 6 Once more, the appearance of crystal structures in the A, B, and D in the D region that match some of our geometries. Comparison regions suggests that the energy differences are low, so that pack- with their work is also included in Table 4. These results show that ing effects can be highly influential. A similar observation can ex- high-level DFT calculations have also encountered the same three plain the appearance of gt, gg, and tg conformers. minima in the main area found by most force fields, and that the

The force fields that changed v1 in cellobiose also did the same for geometry differences with MM3 are negligible; furthermore, they maltose, suggesting that this effect is not restricted to just the b ano- are lower than those found with other force fields. The energy dif- mer. The MM2 variants and GLYCAM are the most notable (Table 4): ferences are within the same order, but the agreement with MM3 again, the difference is produced by an increase in the absolute value is far better than that with Amber94 (Table 4). Regarding their /,w from the regular MM3 value (ca. 50°)to70° to 90°. In OPLS-2005 location, in the A region the DFT minima locate at a spot close to at e = 1 a large shift for v1 appears, but in this case this is due to a ‘ran- those determined by the new force fields (CSFF, GROMOS, GLY- domization’ of its value, sometimes away from the orientation ex- CAM, and OPLS-2005) at e = 1, as well as those of MM3 or pected from the exoanomeric effect. In cellobiose v3 was the other PM3CARB-1. A similar feature was found to occur in the B region, most variable exocyclic, but for maltose, the two most variables although PM3CARB-1, GROMOS and MM4 give the best coinci- are v2 and v20 (Table 4). Regarding v20, those angles having values dence. In the D region, the DFT minima match better with MM4, of around 75° in MM3 at e = 4, increase their magnitude to about MM3, and PM3CARB-1.

Table 4 For a-maltose, geometry of the global minimum (for MM3 at e =4,A gtgg), comparison of the geometries of the conformers minimized by each method with those obtained with MM3 (e = 4), mean absolute deviations (MADs), and range of relative differences (RRDs) against different reference models

Minimum Average difference of Most affected torsionals (average) vs MM3 (e = 4) vs MM3 (e = 1.5) vs Amber94 the 10 exocyclic torsionals (°) MAD RRD MAD RRD MAD RRD

MM3 (e = 1.5) A, gtgg 7.4 ± 11.1 v6 (13°); v20 (11°) 1.76 8.36

MMX (e =4) A, gtgg 7.9 ± 5.0 v1 (14°); v20 (11°) 1.06 4.13

Tinker MM2 (e =4) A, gtgg 8.7 ± 9.1 v1 (35°) 1.06 4.98

Tinker MM2 (e = 1.5) A, gtgg 10.8 ± 10.3 v1 (31°); v6 (11°) 1.35 8.81 1.35 4.77

MM+ (e = 1.5) A, gtgt 4.9 ± 4.9 v1 (15°) 0.89 3.51 2.12 7.32

MM4 (e =4) D, gggg 10.6 ± 11.2 v20 (23°); v1, v30 & v3, (14–17°) 1.99 7.83

MM4 (e = 1.5) D, tggt 10.8 ± 10.1 v20 (22°); v30 , v3, v1 & v40 (12–16°) 2.59 10.4 1.98 8.97 Amber3 B, gtgg 5.6 ± 5.6 Evenly distributed (2–9°) 1.16 4.58 2.24 7.64 1.53 4.58

Amber94 B, gtgg 10.6 ± 6.6 v20 , v2 (17–18°); v30 , v40 , v60 , v3 (12°) 0.92 4.28 2.12 10.5

Amber99 A, gggg 7.7 ± 7.5 v20 & v2 (10–12°) 0.96 5.32 2.36 10.0 0.85 2.35

GLYCAM06 (e =4) A, gtgg 5.4 ± 5.0 v1 (13°) 0.40 1.72 0.64 2.95

GLYCAM06 (e =1) A, tggg 11.3 ± 13.6 v1 (25°); v60 (21°) 1.54 8.97 1.47 6.94 2.20 11.2

CHARMM 19 B, tgtg 11.7 ± 7.3 All but the x, v1 & v6, rest 15–20° 1.59 7.43 2.32 9.77 1.44 5.87 CHARMM 22 A, gttg 13.8 ± 7.5 Evenly distributed (9–20°) 2.43 7.43 3.58 7.71 2.45 5.97

CHARMM 27 B, gtgg 8.6 ± 7.8 v20 & v2 (17°) 1.58 7.03 1.79 9.31 1.41 6.68

CSFF (e =4) A, gtgg 7.5 ± 5.4 x (13°); x’&v1 (10°) 3.04 9.26 2.36 9.17

CSFF (e =1) A, gtgg 10.8 ± 11.7 v60 (23°); v20 , x’&x (12–14°) 3.57 6.65 2.50 9.60 2.90 10.2

OPLS original A, gtgg 10.9 ± 7.4 v20 , v2 (17–20°); v30 , v40 , v60 , v3 (12°) 0.73 4.07 2.09 10.3 0.39 1.46 OPLS 05 (e =4) B, tggt 5.3 ± 5.3 x (14°), rest evenly distributed (1–7°) 2.72 7.79 3.32 8.36

OPLS 05 (e =1) A, tggt 11.8 ± 19.1 v1 (30°), v3, v6 & v40 (13–16°) 2.25 9.95 2.75 11.1 2.99 13.5

GROMOS (e =4) A, gtgg 5.4 ± 5.2 v1 (13°) 2.08 5.95 1.51 5.19

GROMOS (e =1) A, gtgg 8.2 ± 6.8 v20 , v30 , v3 & v40 (11–15°) 2.73 8.63 1.48 6.31 3.21 12.1

PM3CARB-1 D, gtgg 8.1 ± 14.1 v6 & x (12–19°) 1.99 8.99 2.18 4.50 2.56 10.3 DFTa A, tggg 4.6 ± 3.5 Evenly distributed (2–8°) 1.61 5.92 1.88 3.37 2.44 8.68

Units of MAD and RRD are kcal/mol. a For 14 conformers found by Momany et al.35 equivalent to those determined in the current study. C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 2225

3.3. a-Galabiose large standard deviation. The only crystal structure found for the present compound72 has /,w of 98°, 158°, and its hydroxymethyl a-Galabiose has received less attention than the previous disac- groups are disordered. In the major form most structures are gtgt, charides. However, there are some published adiabatic maps in the but in the minor form they are tgtg. The crystal structure falls in the literature.30,59 Again, two minima are found in the main area. Both A minimum, at values close to those found by most force fields. The are close in energy with MM3 at e = 80, and have a 20° separation match is usually better with calculations made at e = 4, and the in the / torsion angle. The displacement is almost 60° in the w tor- best matches are with MM2, MM4, and OPLS-2005, although oth- sion angle,59 which means a better separation than is observed for ers (such as GROMOS, MM3, GLYCAM06, or the semiempirical b-cellobiose. These minima were also named A and B.59 The cur- PM3CARB-1) have very close geometrical data (Fig. 6). rent survey also used 27 starting structures in the A minimum Regarding the exocyclics (Table 5), the force fields closest to and 27 in the B (Fig. 2). The analysis of the minima produced by MM3 (e = 4) are MM+, Amber3, Amber99, GLYCAM06, GROMOS, each force field (Table 1) shows that with most methods, the min- and OPLS-2005 at e = 4. The main exocyclic change is for v1 (Table ima in the A and B regions are quite stable. With GLYCAM at e =4, 5). This angle, influenced by the exoanomeric effect, is about 50° about half of the A structures shifted to B, whereas CHARMM19 in MM3 and most of the other force fields, but MM2 and GLYCAM shifted a similar proportion from B to A (Table 1). The remaining lead it to a value up to 90°, as occurred (with reversed sign) with force fields retained most starting geometries in their original the b-anomer of cellobiose. PM3CARB-1 also shows large differ- form, and only a few were not able to keep some of the original ences, especially regarding v2 and v3. structures. Figure 6 shows the /,w regions for the A and B minima About half of the methods (Table 5) gave A as the preferred calculated with each force field. Table 5 compares the torsion an- minimum energy region, and the other half gave B. A tendency gles of the remaining exocyclics and indicates which of the 54 con- to stabilize the B region was observed when the dielectric constant formers is the global minimum within each calculation. It also was lowered. This extra stabilization changes the global minimum gives the statistical comparison of the force fields with the ‘refer- from the A to the B region when lowering the dielectric constant ence models’. Figure 6 shows that the only force field that gives with OPLS-2005 and GLYCAM06 (Table 5). The stability of the B odd locations for the minima is CHARMM27. The remaining force field conformer was also increased by 0.9–2 kcal/mol with MM3, results fit more or less with each other, especially in the B region, MM4, and GROMOS, but not enough to make it the global mini- which shows very little deviation among different force fields. In mum. CSFF shows a more erratic behavior. The hydroxymethyl the A region, the other CHARMM variants (19 and 22) are only slightly groups of the global minima appear to be in the gg, gt,ortg orien- apart, and GLYCAM06 (e = 1) is within the same region, but with a tation, depending on the force field (Table 5). According to the

Figure 6. Representation of the /,w areas calculated in the A and B regions with each method for a-galabiose. Each ellipse is centered in the average /,w point obtained for each method, and shows axis magnitudes given by the standard deviation. The ellipses are color-coded. Those with cross hatched lines were made at e = 4, whereas the solid or with diagonal line ﬁllings correspond to vacuum calculations. 2226 C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228

Table 5 For a-galabiose, geometry of the global minimum (for MM3 at e =4,A gtgg), comparison of the geometries of the conformers minimized by each method with those obtained with MM3 (e = 4), mean absolute deviations (MAD), and range of relative differences (RRD) against different reference models

Minimum Average difference of Most affected torsionals (average) vs MM3 (e = 4) vs MM3 (e = 1.5) vs Amber94 the 10 exocyclic torsionals (°) MAD RRD MAD RRD MAD RRD

MM3 (e = 1.5) A, gtgg 7.4 ± 9.9 v60 , v2 & v3 (10–12°) 3.06 7.70

MMX (e =4) B, gtgt 8.6 ± 6.7 v1 & v20 (13°); v60 , v2 & v3 (10°) 2.02 4.40

Tinker MM2 (e =4) A, gggg 9.5 ± 13.0 v1 (33°); v6 (17°) 1.09 4.16

Tinker MM2 (e = 1.5) A, gggg 11.2 ± 14.4 v1 (35°); v6 (15°) 1.43 5.94 2.30 5.42

MM+ (e = 1.5) B, gtgt 4.8 ± 6.3 v1 (14°) 1.75 2.83 4.79 10.39

MM4 (e =4) A, gggg 8.6 ± 7.8 v1 (17°); v6, v30 , v3 & v40 (10–13°) 2.23 7.51

MM4 (e = 1.5) A, gggg 9.3 ± 7.5 v6, v30 , v3, v1 & v40 (11–15°) 4.05 11.1 1.27 6.70

Amber3 A, gtgg 5.7 ± 6.2 v20 , v1 & v2 (10–12°) 1.39 2.56 4.44 8.75 1.45 5.34

Amber94 B, gtgt 11.3 ± 9.0 v20 , v2 (18–23°); v30 , v40 , v60 , v3 (13°) 2.48 4.77 5.49 12.3

Amber99 B, gtgt 8.0 ± 6.4 (16°); v1 & v2 (10–12°) 1.01 3.22 3.95 9.08 1.59 3.34

GLYCAM06 (e =4) B, gtgt 5.3 ± 7.2 v1 & v20 (11–13°) 0.98 3.53 1.74 3.78

GLYCAM06 (e =1) A, gtgg 11.2 ± 13.0 v1 (25°); v20 , v2 & v3 (12–16°) 2.77 8.45 1.42 8.31 5.02 11.3

CHARMM 19 B, gttg 12.7 ± 9.1 All but the x & v1, rest 12–22° 3.21 5.53 5.97 12.7 1.36 5.18

CHARMM 22 B, gttg 10.1 ± 8.5 v20 & v2 (18–22°); v60 & v30 (12°) 3.68 10.4 6.74 17.9 1.68 6.93

CHARMM 27 A, tggt 9.8 ± 9.0 v20 & v2 (17–24°); v60 & v30 (12°) 2.10 7.67 4.81 12.1 1.80 8.34 0 CSFF (e =4) B, gtgt 8.0 ± 8.4 v20 , x , x & v1 (10–13°) 1.99 5.79 0.94 3.81 CSFF (e =1) B, ggtg 10.8 ± 16.0 All but x’, rest 9–15° 2.84 15.2 2.96 16.2 4.50 14.1

OPLS original B, gtgt 12.3 ± 9.6 v20 , v2 (20–24°); v30 , v40 , v60 , v3 (14°) 2.99 6.09 6.03 13.8 0.59 2.10 OPLS 05 (e =4) B, tggt 5.2 ± 5.1 Evenly distributed (1–10°) 3.48 9.18 1.90 10.9

OPLS 05 (e =1) A, gtgg 12.8 ± 24.5 v1 (42°), v3, v30 , v2, v6, v40 (10–16°) 4.99 10.1 2.50 9.15 7.27 14.6

GROMOS (e =4) A, gggg 5.3 ± 5.4 v1 (12°) 0.94 4.52 2.56 7.76

GROMOS (e =1) A, gggg 8.5 ± 11.0 v3 (19°) v20 & v30 (11–12°) 3.23 11.9 1.82 8.56 5.34 15.9

PM3CARB-1 A, gggg 12.3 ± 20.7 v2, v3 (24–28°); v60 , v6, v30 (12–15°) 2.07 12.6 2.41 8.78 3.87 13.5

Units of MAD and RRD are kcal/mol.

MAD and RRD, the force fields that show the best energy coinci- Table 6 Cross tables showing the differences in exocyclic torsionals, MAD and RRD between dence (Table 5) with MM3 ( = 4) are GLYCAM06 and GROMOS e six selected force fields, at both high (4) and low (1 or 1.5) dielectric constantsa (at e = 4), and Amber99. The best energy coincidences with MM3 at e = 1.5 are also given by GLYCAM06 and GROMOS, this time MM3 MM4 GLYCAM06 OPLS 2005 CSFF GROMOS working at e = 1, and also by MM4. Difference between the 10 exocyclic torsional angles (°) MM3 — 10.0 4.9 4.8 7.6 5.0 3.4. New force fields MM4 6.8 — 11.9 12.1 14.1 12.4 GLYCAM06 7.4 11.5 — 4.9 8.5 3.0 OPLS 2005 8.2 8.3 10.1 — 7.4 5.2 The current results show that the newer force fields or param- CSFF 7.2 9.4 7.8 7.9 — 8.5 eterizations, such as GROMOS, GLYCAM06, CSFF, MM4 and OPLS- GROMOS 5.8 7.0 8.4 7.7 7.2 — 2005 behave with greater similarity than the older ones, with the MAD (kcal/mol) exception of MM3. These results are based on comparisons of ener- MM3 — 1.66 0.58 2.65 2.16 1.50 gies and geometries with crystal and DFT data. In most cases, the MM4 1.44 — 1.95 3.74 3.30 2.05 GLYCAM06 1.57 1.94 — 2.74 1.77 1.58 results obtained by Amber and CHARMM variants (as well as the OPLS 2005 2.28 2.07 2.56 — 3.66 3.84 old OPLS) in HyperChem are more divergent than those produced CSFF 3.08 3.23 2.60 4.42 — 1.37 by MM3 and the newer force fields. The MM2 variants usually give GROMOS 1.41 1.67 1.90 3.01 2.91 — intermediate results. In order to avoid the use of a single reference RRD (kcal/mol) method (at least at first), a benchmark comparison of the six force MM3 — 6.32 2.32 7.89 7.39 5.52 fields was made, working at e = 4 and separately working at e =1 MM4 6.36 — 5.64 10.00 12.01 8.16 (1.5 for MM3 and MM4). The exocyclic angle differences, MAD GLYCAM06 6.53 8.65 — 7.89 6.53 4.85 OPLS 2005 9.04 9.97 8.48 — 12.82 11.52 and RRD are shown in Table 6 as an average of the results for the CSFF 12.43 12.26 9.37 12.50 — 5.35 three disaccharides. Working at e = 4, similar geometries appear GROMOS 6.55 8.14 7.11 10.45 12.44 — for MM3, GLYCAM06, GROMOS, and OPLS (the closest is between The results are averages of those obtained for b-cellobiose, a-maltose, and a- GLYCAM and GROMOS). On the other hand, MM4 gives the worst galabiose. coincidence. At e = 1/1.5, the coincidence is less, but the best over- a The boldface numbers correspond to calculations at e = 1 or 1.5, whereas the lap is between MM3 and GROMOS (Table 6). Regarding the ener- normal font is used for values calculated at e =4. gies, at e = 4, MM3 and GLYCAM give very similar results, being the only pair with MAD <1 kcal/mol and RRD <4 kcal/mol. GROMOS also gives a good match with them. On the other hand, OPLS shows 4. Conclusions the worst agreement with any other force field, whereas CSFF and MM4 give intermediate values. Also, at e = 1/1.5 the best coinci- The current search of disaccharide conformers indicates that dences are seen between MM3, MM4, GLYCAM, and GROMOS, most of the force fields were able to find minima in all the low-en- whereas OPLS and especially CSFF results are rather different (Ta- ergy regions, and that only a few of them were driven to other min- ble 6). These results indicate that when working with GLYCAM06, ima. Amber94 and the original OPLS force field give similar results GROMOS, or MM3 the results can be compared favorably, as they for disaccharide conformers. The variants of CHARMM give very poor appear to be more homogeneous than those that arise from work- agreement, odd /,w angles for minima, and difficulties in finding ing with other force fields. some minima. C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228 2227

The experimental values available support the results of many to take advantage of the latest developments in force field param- different force fields. However, crystal data agree better with the eterization, bearing in mind that the job of force field developers is calculations made at e = 4 than with those made at lower dielectric to continue improving previous systems. For those who have other constants, whereas the latter match better with DFT results. The main interests, however, it is of importance to find a convergence newer force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) of results for a number of force fields, including some that are agree better with experiment and DFT results than older Amber, available in easy-to-implement, relatively inexpensive software CHARMM or OPLS versions. Thus, new studies with those older force systems. These programs may lack many of the features of the fields should be discouraged. However, it is surprising to find that packages that are used by specialists but make fewer demands an older general-purpose force field like MM3 gives results compa- on the researcher. rable to those of the newer ones (although it appears to be less dielectric constant dependent). The newer force fields look better Acknowledgments than those of MM2 variants (which are still acceptable) and are comparable to those of MM4. PM3CARB-1 also shows more than This work was supported by grants from UBA and CONICET acceptable results on these calculations. Although the present cal- (C.A.S.), and normal research funds from the Agricultural Research culations did not otherwise involve quantum mechanics calcula- Service of the U.S. Department of Agriculture (A.D.F. and G.P.J.). tions, the newer force fields benefit extensively from QM, as their C.A.S. is a Research Member of the National Research Council of parameterizations are based on mimicking QM results. 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