Carbohydrate Research 344 (2009) 2217–2228
Contents lists available at ScienceDirect
Carbohydrate Research
journal homepage: www.elsevier.com/locate/carres
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
b
c
Departamento de Química Orgánica-CIHIDECAR, FCEyN-Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Southern Regional Research Center, U.S. Department of Agriculture, 1100 Robert E. Lee Blvd., New Orleans, LA 70124, USA
Department of Inorganic and Analytical Chemistry, Budapest University of Technology, Szent Gellért tér 4, Budapest H-1521, Hungary
a r t i c l e
i n f o
Article history:
Received 26 May 2009
Received in revised form 13 August 2009
Accepted 18 August 2009
Available online 22 August 2009
Keywords:
Force field
Disaccharides
Molecular mechanics
Cellobiose
Maltose
Galabiose
a b s t r a c t
Eighteen empirical force fields and the semi-empirical quantum method PM3CARB-1 were compared for
studying b-cellobiose, a-maltose, and a-galabiose [a-D-Galp-(1?4)-a-D-Galp]. For each disaccharide, the
energies of 54 conformers with differing hydroxymethyl, hydroxyl, and glycosidic linkage orientations
were minimized by the different methods, some at two dielectric constants. By comparing these results
and the available crystal structure data and/or higher level density functional theory results, it was concluded that the newer parameterizations for force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF) give
results that are reasonably similar to each other, whereas the older parameterizations for Amber, CHARMM
or OPLS were more divergent. However, MM3, an older force field, gave energy and geometry values comparable to those of the newer parameterizations, but with less sensitivity to dielectric constant values.
These systems worked better than MM2 variants, which were still acceptable. PM3CARB-1 also gave adequate results in terms of linkage and exocyclic torsion angles. GROMOS, GLYCAM06, and MM3 appear to
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
Knowledge of the three-dimensional structures of disaccharides
is essential for understanding biological and physical functions.
Determinations of the conformational preferences and variability
of disaccharides are useful not only for the disaccharides themselves, but can often also apply to oligo- and polysaccharides having the same primary structure.1 This understanding can be aided
by reliable molecular modeling. In the beginning, computerized
disaccharide modeling relied on very simple models that varied
the torsion angles of the glycosidic linkage but not the geometries
of the monosaccharide residues. Back then, structures were rated
as either ‘allowed’ or ‘disallowed’ based on interatomic distances.
Later, potential energies were calculated for the rigid residue models based on van der Waals forces, twisting about bonds, and sometimes, emulation of hydrogen bonding. The HSEA2 and PFOS3
potential energy functions for carbohydrates employed torsional
potentials that explicitly accounted for the exoanomeric effect
but still used rigid residues. This was a problem because the results
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
* Corresponding author. Tel./fax: +54 11 4576 3346.
E-mail address: [email protected] (C.A. Stortz).
0008-6215/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.carres.2009.08.019
optimization (flexible residues) was just becoming available, but
some early versions did not specifically treat the exoanomeric effect. The anomeric effect is thought to arise from a combination of
electrostatic effects and rearrangement of the electronic structure,
giving stabilization to certain conformations and not others. Such
problems are the domain of electronic structure theory (quantum
mechanics or QM), which also has the capacity to describe all other
molecular properties, including hydrogen bonding. In principle,
quantum mechanics could answer most of the questions being
asked in MM studies. Apparent success with the Hartree–Fock
(HF) methods and modestly sized basis sets relies too much on
cancellation of errors, limiting the possibility of improvement.
Density functional theory (DFT) can provide reasonable results
for saccharides,4 but at present it is also expensive in terms of computer time and memory for large-scale calculations. Correlated
wavefunction theory (e.g., MP2 or CCSD(T)) is even more expensive. Although QM methods continue to improve, there is still a
great body of work for which MM methods are more suitable.
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.
Additionally, there are significant bond length variations associated with the
anomeric effect, and this has also been parameterized for some force fields.
2218
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
MM methods now often employ parameters that allow the MM
software to mimic the results from QM studies on fragments of
disaccharides. This allows MM to account for many factors, including the exoanomeric effect.
Disaccharide analysis by modeling is a large-scale problem even
if there is no worry about changes in the form of the pyranosyl
rings. Disaccharide shapes are analyzed either by generating a
Ramachandran-like conformational map (contour map of energy
vs / and w), or just by finding the energies of isolated minima. In
either case, such studies might explain experimental results. While
it is often considered that the glycosidic torsion angles / and w
(Fig. 1) are the main variables of shape, there will be numerous stable conformers (‘multiple minima’)5 with different energies resulting from different combinations of the orientations of the primary
and secondary hydroxyl groups. Preference for the given values of
/ and w will often depend on a particular combination of exocyclic
group orientations. For example, cellobiose has, in addition to / and
w, 10 exocyclic bonds about which rotation can occur. If each is allowed three staggered orientations, there would be 310 = 59,049
possible structures (for each /,w point). Many would not be stable,
but unless all are evaluated, it could be that the lowest energy value
will not have been found. In modeling studies, a frequent task is to
compare the depths of different energy wells on a /,w surface. In
such work it is necessary to give a reasonably complete treatment
of the exocyclic group orientations for each well to get an answer
that fully represents the particular computational method.
Flexible residue analysis3,6–8 of disaccharides started around
1979 and by the late 1980s the first fully relaxed energy maps of
numerous disaccharides had been constructed.9–11 Except for the
early Melberg and Rasmussen calculations,6–8,12 most were carried
out with Allinger’s MM2,13 by carbohydrate-specific variants like
MM2CARB,3 or with CHARMM14 and the carbohydrate parameters
of Ha et al.15 Subsequently, MM3, an all-atom force field with upgraded parameterization for anomeric effects on torsional energies
and bond lengths as well as hydrogen bonding,16 was released and
used for many disaccharide studies.17–20 Earlier in the 1980s, many
new force fields were developed, some of them especially intended
for molecular dynamics (MD) in general (like GROMOS21). Others
targeted proteins or nucleic acids, such as Amber,22 CHARMM,18 and
OPLS.23 These force fields have been updated with parameterizations that covered carbohydrates.24,25 Recently GLYCAM,26 a
parameterization for carbohydrates of the Amber force field, was
updated as a stand-alone, general-purpose force field useful for
molecules in addition to carbohydrates (GLYCAM06).27 Other special parameterizations of force fields for carbohydrates have also
appeared recently.28,29 QM methods have also been used directly.
Initially French et al. made adiabatic maps of disaccharide analogs
at the HF/6–31G* level,30 and then used them in a simple hybrid
QM/MM method.31 The hybrid method was especially useful for
modeling sucrose. The conformational space of the desialyated Lewis X trisaccharide and its analogues was probed with HF and
MM2* levels of theory.32 Momany and co-workers studied different conformations of maltose and cellobiose using DFT.33,34 Even
though very large amounts of computer time were required, later
QM studies yielded full maps of disaccharides, considered greater
numbers of conformers, or even undertook larger oligosaccharides.35–39
Despite the improved MM methods, the chosen force field still
influences the results. In 1998, Pérez et al. analyzed several monosaccharides and a single disaccharide with different force fields
that were available then,40 focusing more on comparing the force
fields to each other rather than on comparisons with the experimental values. Since then, only a few comparisons of MM methods
have been published41 in spite of the new parameterizations and
functional variants for carbohydrates.24–29 Comparison of HF, hybrid DFT and MM2* results showed the difficulties in predicting
energies for carbohydrates with MM methods,42 attributed to their
densely packed, highly polar functional groups, and the dependence of conformational energies on stereoelectronic effects.
MM2* gave good qualitative results for the lowest energy rotamers
of monosaccharides, in spite of showing an energetically compressed conformational space with incorrectly ordered rotamers
in the higher energy region. Other comparisons with several force
fields have been made for QM results for glucose.43 Comparisons
have also been made with higher saccharides.32
Herein, we compare the performance of 18 different force fields
or variants, some of them at two different dielectric constants,
working with a set of 54 conformers each of b-cellobiose, a-maltose, and a-galabiose [a-D-Galp-(1?4)-a-D-Galp] (Fig. 1) with varying hydroxymethyl and hydroxyl group orientations. Although
PM3 and other semiempirical molecular orbital methods have
been shown to fail with carbohydrates,44 a variant parameterized
for carbohydrates (PM3CARB-145) has been issued. The performance comparison with this semiempirical method is also
included.
In this comparison, we have not included the effects of explicit
solvation. As some force fields have been parameterized to reproduce the experimental data in solution, it might be considered
somewhat inappropriate to compare such force fields with those
that did not include explicit water molecules during parameterization. We have proceeded on the assumption that, in principle, such
modifications to the force field should be minor (or not needed at
all) so that the correct interpretation of the effect of explicit solvent
on the simulated system can be observed.
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
Figure 1. The disaccharides studied in this work. The nomenclature of the torsion
angles is indicated for b-cellobiose.
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
developers consider such predictions as inappropriate and discourage the use of
elevated dielectric constants.
2219
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
termination criterion was 100 times stricter than the default, that is,
the calculation was stopped when the average movement was less
than 2 106 Å. Each resulting structure was confirmed as a minimum with a full matrix minimization and frequency calculation.
(b) Using the program Tinker 4.2 (Washington University),47 with
force fields MM2 and MM3 at e = 1.5 and e = 4. The final gradient
was kept at 0.01 kcal mol1 Å1. (c) Using PCModel 9.2 (Serena Software), for force field MMX at e = 4, using default termination conditions. (d) Using Hyperchem 848 for the force fields MM+, Amber (3,
94 and 99), CHARMM (17, 22, and 27) and original OPLS, and with
the semiempirical method, PM3CARB-1.45 In all the Hyperchem
MM cases the dielectric constant was kept at its default value, and
the final gradient was set at 0.01 kcal mol1 Å1. (e) Using native
MM4,49,50 with dielectric constants of 1.5 and 4. The termination
condition was average movement <2 106. This was 100 times
stricter than the default. (f) Using MacroModel51 with the OPLS2005 force field52 and the Polak–Ribiere conjugate gradient minimizer and dielectric constants of 1 and 4.§ The termination condition
was a gradient <1.2 104 kcal mol1 Å1. This is 100 times stricter
than the default condition. (g) Using native Amber1053 with the GLYCAM0627 parameters, the limited-memory Broyden–Fletcher–Goldfarb–Shanno quasi-Newton minimizer, and dielectric constants of
1 and 4. We used the smallest available termination criterion, a gradient <1.0 105 kcal mol1 Å1. This is 10 times stricter than the
default. (h) Using the native CHARMM program and CSFF54 variant of
the force field with its default termination criteria and the adopted
basis Newton–Raphson minimizer. (i) Using native Gromacs55 with
the GROMOS96 force field,21,56 and both the 45a428 and the 53a657
parameter sets with the default termination criteria. As both give
practically the same results, only those of the 45a4 set (recommended for carbohydrates) are included in this paper.
2.2. Nomenclature and starting geometries
The torsion angle x is defined by the atoms O-5–C-5–C-6–O-6,
primed for the non-reducing end. As usual, the rotamers are classified as gt (x 60°), tg (x 180°) or gg (x –60°). For the disaccharide, the orientation of the hydroxymethyl groups is
expressed with the non-reducing end first (e.g., gggt indicates a
non-reducing end with gg orientation, and a reducing end with gt
orientation). The glycosidic torsion angles / and w are defined by
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 vn,
defined by the atoms H-n–C-n–O-n–H(O)-n, whereas v6 is defined
by the atoms C-5–C-6–O-6–H(O)-6, primed when appropriate
(Fig. 1). All starting structures had their pyranosyl rings in the most
stable, 4C1 conformation. The nomenclature for the regions of minimal energy (A, B, and D) follows the conventions used previously58,59 for the three disaccharides (Fig. 2).
The 54 starting conformers for cellobiose and galabiose consisted of 27 in the A region and 27 in the B region. Each set of 27
corresponded to three combinations of OH orientations, combined
with each of the 9 combinations of both hydroxymethyl groups in
gt, gg, or tg orientation. For maltose, which has three main regions
of minimum energy (A, B, and D, Fig. 2), only two combinations of
OH orientations were used for each combination of hydroxymethyl
rotamers. The three conformers (two for maltose) were chosen
after a preliminary study made with MM3 at e = 4, where the
§
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,
studies based on a dielectric constant of 4 are not strictly comparable. In the case of
MMn, a dielectric constant of 4 corresponds to a reduction of the electrostatic
energies by a factor of (1.5/4) or 0.375. For methods that assume a dielectric constant
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
interactions and on an extra term that does not depend on the dielectric constant.50
energies of hundreds of rotamers were calculated: those with the
lowest energy within each set of the /,w region and hydroxymethyl rotamers were chosen. As no exhaustive search was made
for all 6561 combinations of OH group orientations, conformers
with lower energy could exist. However, it was not our purpose
here to determine the particular ideal conformers, but to only provide a range of stable starting structures that can be tested with
the different methods. In order to obtain those MM3-minimized
structures, the input structures contained the following /,w angles: for cellobiose, 75°, 123° (A region), and 88°, 163° (B region); for maltose, 98°, 144° (A region), 68°, 168° (B region), and
95°, 75° (D region); for galabiose, 102°, 160° (A region) and 76°,
105° (B region). The starting geometry for the D region of maltose
was chosen to be far from its final point, in order to avoid drifts to
the A region. The MM3 (e = 4) minimized structures were used as
starting points for the calculations with other force fields and programs. In each case, the energies and geometries of the resulting,
optimized conformers were compared within themselves. Besides
the A and B minima for cellobiose, a set of nine cellobiose ‘flipped’
conformers (i.e., those in the region around /,w = 60°, 120°
(Fig. 2) was created. All nine combinations of hydroxymethyl orientations were represented, with the secondary hydroxyl groups
set in an anticlockwise (rr0 ) arrangement of hydrogen bonds.34,60
For these ‘flipped’ structures, the v6 were chosen to give the lowest
energy using MM3 at e = 1.5.
2.3. Indicators from the calculations
The following definitions4 of the relative energies were used
DEmodel ðconf i ; conf ref Þ ¼ Emodel ðconf i Þ Emodel ðconf ref Þ
ð1Þ
is the relative energy of the ith conformer, confi compared to the energy of a reference conformer, confref using a given model chemistry
(force field, program, and e).
DDEmodel
Amodel B ðconf i ; conf ref Þ
¼ DEmodel A ðconf i ; conf ref Þ DEmodel B ðconf i ; conf ref Þ
ð2Þ
is the relative energy difference of the ith conformer calculated with
two different model chemistries.
The model and reference conformer dependent mean absolute
deviation (MAD) is defined as
MADmodel
¼
Amodel B ðconf ref Þ
n
1 X
jDDEmodel
n 1 i¼1
Amodel B ðconf i ; conf ref Þj
ð3Þ
Note that within a given test set of conformers the MAD between the two compared models (model A and model B) depends
on the choice of the reference conformers. One way to eliminate
this problem is to compare the range of DDEmodel Amodel B(confi,
confr) values of Eq. 2. The range of the relative difference was defined as RRD = max DDE min DDE. The reference conformers
for maltose and galabiose had the lowest energy with MM3
(e = 4) along with the gtgg orientation, whereas for cellobiose the
reference structure is gtgt.
3. Results and discussion
The 54 conformers of each of the three disaccharides (Fig. 1)
were geometry-optimized with different methods (method = force
field + dielectric constant + program). Table 1 shows the number of
conformers that remained in their original region of minimum energy, that retained their x angles (within ±60°), and that were not
identical to another conformer in the list. With the three disaccharides, 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
program. Thus, only the results obtained with native MM3 are
shown below.
3.1. b-Cellobiose
There are numerous studies of the adiabatic map of b-cellobiose.7,12,18,20,36,38,58 Two minima, very close to each other in energy,
have similar / torsion angles but are displaced about 40° in the w
torsion angle. These minima were designated as A and B.38,58 The
current survey, made with 27 A conformers and 27 B conformers
(Fig. 2) showed, at least with MM3, that every hydroxymethyl orientation can be stable. Table 1 shows that the 27 minima in the A
region are quite stable regardless of force field, as only seven instances of departure from the original structure occurred with
the MM methods. Besides, six A minima were unstable with
PM3CARB-1. Conformers in the B region were also stable when
minimized by most force fields, but quite a few converted to the
A region with GLYCAM06, CHARMM19 or OPLS-2005. Figure 3 shows
the /,w regions for the A and B minima calculated with each force
field. Table 2 compares the torsion angles of the remaining exocyclic bonds (v20 , v30 , v40 , v60 , x0 , v1, v2, v3, v6, and x), indicates
which of the 54 conformers is the global minimum within each calculation, and gives the statistical comparison of the force fields
with the ‘reference models’. Figure 3 shows that the CHARMM variants give rather different /,w locations, especially CHARMM27. Allinger’s MM force fields all gave similar /,w locations, and Amber3
minima are also close by. The newer force fields’ minima are closer
to those of the MMn force fields when working at e = 4.
Keeping in mind that the packing effects can influence the /,w
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
shows /,w values of 76°, 132°, in the A region. MM2 and especially GROMOS (e = 1) give A minima closest to this value (Fig. 3),
although MM3 and the newer force fields CSFF, OPLS-2005, and
GLYCAM06 (at e = 1) are also very close. Both hydroxymethyl
groups in the crystal have the gt orientation. The only method that
Table 1
Number of conformers remaining after minimization with each methoda
Method
MM3 (e = 4)
MM3 (e = 1.5)
MMX (e = 4)
Tinker MM2 (e = 4)
Tinker MM2 (e = 1.5)
MM+ (e = 1.5)
MM4 (e = 4)
MM4 (e = 1.5)
Amber3
Amber94
Amber99
GLYCAM06 (e = 4)
GLYCAM 06 (e = 1)
CHARMM 19
CHARMM 22
CHARMM 27
CSFF (e = 4)
CSFF (e = 1)
OPLS original
OPLS 05 (e = 4)
OPLS 05 (e = 1)
GROMOS (e = 4)
GROMOS (e = 1)
PM3CARB-1
a-Maltose
b-Cellobiose
a-Galabiose
A
B
A
B
D
A
B
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
26e
27
22b,d
27
27
26b
27
27
21b
27
26b
24b
27
27
24b
26d
26d
27
24b
27
11d
6d
8d
27
18b,e
22d
19b,d
24b
14d
9d
27
27
18b,d
18
17b
8d
17b
17b
18
16b,d
14d
16d
11d
13e
17d
17b
2d
18
0d
18
17b
14d
16d,e
10b,d,e
18
17b
11b,d,e
18
15b,c
18
11d
10d
17d
17b
16b
18
18
18
9d
8b,d
18
0d
14e
4d
10b,d
16d
18
13b,d
18
18
9b,d,e
18
16b,d
18
18
18
18
16d
15d
18
17d
17e
5d
8d
17d
2d
15e
10d
11d
15d
15d
16d
18
14d
13d,e
27
24b,c,d
27
27
26b
27
26d
27
27
27
27
13d
24b,d
27
27
27
22d
26d
27
26d
26b
27
27
20b
27
26d
27
24d
23d
27
27
25d
27
27
27
27
25b
14d
27
27
27
22b,d
27
27
20b,d
27
26b
23b,d
a
The number of starting conformers for cellobiose and galabiose was 27 for each of
the A and B regions, and for maltose 18 in each of the A, B, and D regions.
The remaining conformers were lost due to: b passage to other existing conformers
in the same minimum energy region; c imaginary frequencies; d passage to another
minimum energy region; e rotation of one of the hydroxymethyl groups of more
than 60°.
provided an A-gtgt conformer as the global minimum was MM3 at
e = 4 (Table 2). However, by most of the other methods, the most
stable A-gtgt conformer had energies 0.121.45 kcal/mol above
the global minimum. The only methods that gave higher energies
were OPLS-2005, MM4, CSFF, and GLYCAM06 when working at
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.
2221
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
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
MM3 (e = 1.5)
MMX (e = 4)
Tinker MM2 (e = 4)
Tinker MM2 (e = 1.5)
MM+ (e = 1.5)
MM4 (e = 4)
MM4 (e = 1.5)
Amber3
Amber94
Amber99
GLYCAM06 (e = 4)
GLYCAM06 (e = 1)
CHARMM 19
CHARMM 22
CHARMM 27
CSFF (e = 4)
CSFF (e = 1)
OPLS original
OPLS 05 (e = 4)
OPLS 05 (e = 1)
GROMOS (e = 4)
GROMOS (e = 1)
PM3CARB-1
A, gttg
B, gtgt
B, gttg
B, tgtg
B, gtgg
A, gtgg
B, gtgg
A, gtgg
A, gtgg
A, gtgg
A, gtgg
A, tgtg
A, tgtg
B, gttg
B, gggt
A, gggg
B, gtgg
A, gtgg
A, tggt
A, gttg
A, gtgg
A, gttg
A, gtgg
Average difference of
the 10 exocyclic torsionals (°)
Most affected torsionals (average)
5.4 ± 3.0
8.8 ± 11.3
10.0 ± 12.9
10.9 ± 12.2
4.5 ± 5.3
10.7 ± 6.1
9.2 ± 5.7
4.6 ± 4.4
10.3 ± 13.8
5.9 ± 6.4
4.0 ± 5.1
8.2 ± 10.8
11.8 ± 10.9
12.1 ± 6.6
8.2 ± 15.2
7.3 ± 5.1
7.6 ± 17.7
10.7 ± 13.5
3.6 ± 4.2
8.1 ± 6.1
4.3 ± 5.3
7.7 ± 6.4
7.7 ± 8.9
Evenly distributed (3-8°)
v3 (30°); v1 (13°)
v1 (40°)
v1 (45°); v6 (10°)
v3 (13°)
All but the x (v20 , v30 & v2, 16-17°)
v30 , v20 , v40 , v2 & v3 (11-15°)
Evenly distributed (2-9°)
v3 (30°); v40 (11°)
v3 (13°); x0 (10°)
v1 (15°)
v1 (38°)
v3 (36°), v30 , v40 , v20 , v6, v60 (10-15°)
Evenly distributed (8-16°)
v3 (34°); x0 (11°)
x’, x & v3 (11°)
x (18°), rest evenly distributed (3-9°)
v3 (36°); v40 (12°)
x (11°), rest evenly distributed (2-6°)
v3, v2 & v40 (11-13°)
v3 (12°)
v3 (20°), v40 (11°)
v1, v3 & x (12-15°)
vs MM3 (e = 4)
MAD
RRD
0.93
1.15
0.95
1.30
1.38
0.74
1.58
0.98
0.77
0.90
0.35
2.22
2.13
1.79
2.75
1.43
4.20
0.85
1.62
1.52
1.49
1.55
1.23
5.37
2.04
4.60
5.44
2.87
3.62
6.63
2.19
4.02
4.37
1.70
7.56
4.60
4.23
5.50
7.10
10.9
4.23
6.71
7.07
6.09
6.25
5.61
vs MM3 (e = 1.5)
MAD
RRD
0.81
1.08
2.77
5.35
1.07
1.03
1.56
1.67
3.42
4.99
8.53
8.83
1.82
1.78
1.43
2.73
4.34
3.33
5.28
10.4
3.79
1.60
11.5
8.15
1.59
6.90
0.93
1.08
4.79
5.53
vs Amber94
MAD
RRD
1.15
4.22
0.41
0.61
2.41
2.10
2.20
2.81
0.74
4.38
0.40
2.14
1.96
0.97
1.98
1.50
1.22
2.68
10.1
6.58
7.61
6.68
4.00
12.6
1.68
9.51
9.81
2.50
8.47
6.16
Units of MAD and RRD are kcal/mol.
diffraction studies have been carried out on related molecules,
such as higher oligomers, derivatives with the hydroxyl groups
partly or totally substituted, and with solvates that incorporate
water, MeOH, or EtOH.62 Most of the fully O-acetylated crystalline
products appear in the A region (/ 75°, w –104° to 110°), as
gggt rotamers. The non-reducing end and central residue of cellotriose undecaacetate are linked with bonds having / = 98°,
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
161°).
Although most of the hydroxymethyl groups are gt, there are
some (especially at the reducing end) appearing as gg. Only one
example of a tg hydroxymethyl group has been found64 in molecules related to cellulose despite the rotamer being found in native
cellulose.65 The appearance of crystalline forms in the A and B minimum energy regions, and with gt, tg, or gg orientations suggests
very low differences in energy among the conformations.
Regarding the exocyclic groups (Table 2), the force fields closest
to MM3 (e = 4) are MM+, Amber3, Amber99, GROMOS, GLYCAM06,
and OPLS-2005 at e = 4. The two main exocyclics that change are v1
and v3 (Table 2). Susceptible to the exoanomeric effect, v1 is about
50° in MM3 and most of the other force fields. However, MM2 and
GLYCAM lead it to a value up to 90°. The other major variability
was for v3, especially in the B region. Some force fields (notably
the 19 and 27 versions of CHARMM, the 94 and 99 versions of Amber,
and MMX) force it close to 50°, whereas the other force fields place
H(O)-3 in a variety of orientations depending on the other hydroxyl
orientations. The behavior of the Amber variants with regard to v2
is noteworthy. Minimization yielded two conformers with exactly
the same energy and the same absolute value of v2. However, the
sign of the v2 angle is different, even though all the remaining angles are identical. The H-bond interaction of H(O)-2 with O-3 or
with O-1 gives exactly the same total energy to the whole
molecule.
Most force fields (Table 2) show the A region to have a lower energy 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, or tg orientation, depending on the force
field (Table 2). According to the MAD and RRD, the force field that
shows the best energy coincidence (Table 2) with MM3 (e = 4) is
GLYCAM06 (e = 4). The Amber variants and MM4 also show a good
match. It is noteworthy that the Amber variants, although made at
the default dielectric constant (e = 1), match better with the results
of MM3 at e = 4 than with those made at e = 1.5. A similar effect
was found with CHARMM. Furthermore, Amber94 shows a good
match (Table 2) with GLYCAM06 (e = 4) but not with GLYCAM06
at e = 1.
DFT studies of b-cellobiose showed34 that the global minimum
corresponds to a conformer located within an unusual /,w region,
still influenced by the exoanomeric effect but sterically not very
advantageous.20 This region, around /,w = 60°, 120°, received different designations as ‘side-of-the-map’,20 ‘flipped’,34 or ‘folded’.36
The original B3LYP/6-311++G(d,p) results34 were also confirmed by
less-expensive HF/6-31G(d) and B3LYP/6-31+G(d) calculations.36,38It has been explained that the great stability of this conformer, which does not correspond to any of the known crystalline
forms, is due to an anti-clockwise arrangement of hydrogen bonds
involving both sugar rings.60 Thus, it is expected that a force field
working at low dielectric constants with good parameterization
of hydrogen bonding would also favor the flipped forms. French
and Johnson observed66 that the numerous flipped conformers all
fell into a smaller part of the /,w space than for the other regions,
something that might also occur with the MM force fields.
Nine conformers of b-cellobiose in the flipped region (Fig. 2)
with different arrangements of hydroxymethyl groups but the
same anti-clockwise arrangement of the secondary hydroxyl
groups were studied as above. Results are shown in Table 3, and
Figure 4 compares the location of the /,w angles with those of
the DFT calculation.34 Table 3 shows that the older force fields
(Amber, CHARMM, MM2 variants, original OPLS) did not indicate
greater stability for the flipped conformers. On the other hand,
the newer force fields MM4, GLYCAM06, CSFF, OPLS-2005, and
GROMOS show one flipped conformer as the most stable at low
Table 3
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
DE (kcal/mol)
Minimum
DFT (from Ref. 34)
–2.55
gggg
MM3 (e = 4)
MM3 (e = 1.5)
MMX (e = 4)
Tinker MM2 (e = 4)
Tinker MM2 (e = 1.5)
MM+ (e = 1.5)
MM4 (e = 4)
MM4 (e = 1.5)
Amber3
Amber94
Amber99
GLYCAM06 (e = 4)
GLYCAM 06 (e = 1)
CHARMM 19
CHARMM 22
CHARMM 27
CSFF (e = 4)
CSFF (e = 1)
OPLS original
OPLS 05 (e = 4)
OPLS 05 (e = 1)
GROMOS (e = 4)
GROMOS (e = 1)
PM3CARB-1
3.41 (4.73)a
0.00 (2.30)a
1.88
1.49
0.39
2.45
–0.92
–2.90
1.43
2.78
2.47
0.77
–4.66
2.15
5.64
3.52
1.80
–1.51
3.50
–0.01
–5.07
1.47
–6.19
–0.35
gggg
gttg
gtgt
gttg
gttg
gtgt
gttg
gttg
gggg
gtgg
gggg
gggg
gggg
tggg
gttg
gggg
gggg
gggg
gtgt
tgtg
gggg
gtgg
gggg
gggg
The hydroxymethyl geometries of the most stable conformers are also indicated.
a
In parentheses, free energy.
dielectric constant, with a higher energy at e = 4. At the same time,
MM3 at e = 1.5 gives equal energies for the most stable conformers
in each region (Table 3). PM3CARB-1 also predicts more stability
for the flipped conformer. The energy difference predicted by
DFT is closer to that obtained by MM4, and also close to those predicted (in order) by CSFF, GLYCAM06, PM3CARB-1, OPLS-2005,
MM3, MM2, and GROMOS. However, MM4 and OPLS-2005 show
a disadvantageous feature: even at e = 4 a flipped conformer is
more stable than the ‘normal’ forms. Most of the newer force fields
show the same preferred conformer as DFT, gggg. On the other
hand, the values of the /,w angles found by DFT34 (after conversion
from H-based angles to C/O based angles) shown in Figure 4 match
excellently with those of MM3, GROMOS, and MM4 and are also in
good agreement with the other new force fields at e = 1. While the
location of the minima from the various force fields (except MM3)
did not coincide exactly with the DFT results when working at e = 4
(Fig. 4), most discrepancies are minor in terms of degrees. As observed with B3LYP/6-31+G(d) calculations, all the flipped conformers fall into a smaller part of /,w space.66
3.2. a-Maltose
The adiabatic map of a-maltose has also been studied extensively.6,10,17,20,58 Although it was also thought that only two minima appear in the lower-energy region, an adjacent third
minimum has been described. According to older MM3 calculations58 minima A and B differ by about 30° in / and 25° in w, that
is, they are more separated in / than in w. Minimum A appeared to
have slightly lower energy. However, a third minimum (D), with
higher energy has been found, occupying a region which is 20° in
/ and 35° in w from A, further away from B.58 The current work
was carried out with 18 minima each in the A, B, and D regions
(Fig. 2), including all nine staggered combinations of hydroxymethyl orientations. The closeness of the three minima allows
many passages from one minimum energy region to another (Table
1). Thus, no method (besides MM3 and GROMOS at e = 4) was able
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
to keep the original 54 conformers. CHARMM27 did not keep any A
minimum conformers, and CHARMM19 kept only a few. In contrast,
CHARMM22 kept all the A minimum conformers, the B conformers
shifted to A, and only two D conformers were stable. PM3CARB1, Amber99, and CHARMM27 showed a tendency to shift tg conformations to gt and gg rotamers. GLYCAM06 and CSFF showed many
2223
shifts of D and B conformers to the A region, whereas for Amber
versions the A conformers shifted somewhere else. Figure 5 shows
the distribution of /,w angles in each region: in the D region some
methods give very wide ellipses, suggesting a great degree of /,w
variability depending upon hydroxyl and hydroxymethyl group
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
gives /,w values distant from the average values. In the A and D regions the newer force fields (GROMOS, GLYCAM, OPLS-2005 and
CSFF) tend to form differentiated subregions at e = 1 and e = 4. Table 4 compares the torsion angles, shows which of the 54 conformers is the global minimum for each method, and gives the statistics
for comparison of the force fields with the ‘reference models’.
The crystal structure of a-maltose67 has /,w of 116°, 118°,
matching our D region /,w values determined using MM4 and is
not far from the minimum given by PM3CARB-1 (Fig. 5). These
two methods were the only ones to find the D region to have the
lowest energy (Table 4). The crystal structures of the hydrates of
b-maltose and its methyl glycoside also fall within the D region,68
right in the middle of the MM4 and PM3CARB-1 ovals (Fig. 5). For
these three compounds, the hydroxymethyl rotamers were either
gtgt or gtgg. On the other hand, acylated derivatives of b-maltose69,70 appear in the B region, with /,w values close to those of
MM4. Their hydroxymethyl groups appeared in various orientations, including tg for the non-reducing end.69 Finally, higher oligomers and phenyl b-maltoside appear in the A region, and the
hydroxymethyl groups are gg or gt, depending on the compound.71
Once more, the appearance of crystal structures in the A, B, and D
regions suggests that the energy differences are low, so that packing effects can be highly influential. A similar observation can explain the appearance of gt, gg, and tg conformers.
The force fields that changed v1 in cellobiose also did the same for
maltose, suggesting that this effect is not restricted to just the b anomer. The MM2 variants and GLYCAM are the most notable (Table 4):
again, the difference is produced by an increase in the absolute value
from the regular MM3 value (ca. 50°) to 70° to 90°. In OPLS-2005
at e = 1 a large shift for v1 appears, but in this case this is due to a ‘randomization’ of its value, sometimes away from the orientation expected from the exoanomeric effect. In cellobiose v3 was the other
most variable exocyclic, but for maltose, the two most variables
are v2 and v20 (Table 4). Regarding v20 , those angles having values
of around 75° in MM3 at e = 4, increase their magnitude to about
100° at lower dielectric constants, and to even higher absolute values (150°) with MM4. Amber and other force fields have a smaller
change of these v20 values, but also change other v values so the average is also high. Using MM3, almost all conformers have a v2 with
values of either 65° or 165°. They do not change very much with
other force fields (e.g., Allinger MMn variants or GLYCAM), but they
switch to values of 50–58° and 173–180°, respectively, with Amber94, Amber99, CHARMM27, or OPLS. For maltose, most force fields
(Table 4) show some A and gtgg conformer as the preferred minimum. Amber3 and CHARMM27 show the same gtgg rotamer as preferred, but in the B region. Other CHARMM variants, Amber94 and
OPLS-2005 at e = 4 also give a B minimum. Additionally, MM4 and
PM3CARB-1 show a D minimum. It should be noted, however,
(Fig. 5) that these D minima are located closer to the A region than
those produced by other methods (with the exception of GROMOS
at e = 1). GLYCAM06 (e = 4) again shows the best coincidence in energy (Table 4) with MM3 (e = 4). The Amber variants again show a
good match, but MM4 does not.
Momany and co-workers have studied several conformers of amaltose by DFT.35 From their supplementary material we were
able to pick 3 conformers in the A region, 5 in the B region and 6
in the D region that match some of our geometries. Comparison
with their work is also included in Table 4. These results show that
high-level DFT calculations have also encountered the same three
minima in the main area found by most force fields, and that the
geometry differences with MM3 are negligible; furthermore, they
are lower than those found with other force fields. The energy differences are within the same order, but the agreement with MM3
is far better than that with Amber94 (Table 4). Regarding their /,w
location, in the A region the DFT minima locate at a spot close to
those determined by the new force fields (CSFF, GROMOS, GLYCAM, and OPLS-2005) at e = 1, as well as those of MM3 or
PM3CARB-1. A similar feature was found to occur in the B region,
although PM3CARB-1, GROMOS and MM4 give the best coincidence. In the D region, the DFT minima match better with MM4,
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
MM3 (e = 1.5)
MMX (e = 4)
Tinker MM2 (e = 4)
Tinker MM2 (e = 1.5)
MM+ (e = 1.5)
MM4 (e = 4)
MM4 (e = 1.5)
Amber3
Amber94
Amber99
GLYCAM06 (e = 4)
GLYCAM06 (e = 1)
CHARMM 19
CHARMM 22
CHARMM 27
CSFF (e = 4)
CSFF (e = 1)
OPLS original
OPLS 05 (e = 4)
OPLS 05 (e = 1)
GROMOS (e = 4)
GROMOS (e = 1)
PM3CARB-1
DFTa
A, gtgg
A, gtgg
A, gtgg
A, gtgg
A, gtgt
D, gggg
D, tggt
B, gtgg
B, gtgg
A, gggg
A, gtgg
A, tggg
B, tgtg
A, gttg
B, gtgg
A, gtgg
A, gtgg
A, gtgg
B, tggt
A, tggt
A, gtgg
A, gtgg
D, gtgg
A, tggg
Average difference of
the 10 exocyclic torsionals (°)
Most affected torsionals (average)
7.4 ± 11.1
7.9 ± 5.0
8.7 ± 9.1
10.8 ± 10.3
4.9 ± 4.9
10.6 ± 11.2
10.8 ± 10.1
5.6 ± 5.6
10.6 ± 6.6
7.7 ± 7.5
5.4 ± 5.0
11.3 ± 13.6
11.7 ± 7.3
13.8 ± 7.5
8.6 ± 7.8
7.5 ± 5.4
10.8 ± 11.7
10.9 ± 7.4
5.3 ± 5.3
11.8 ± 19.1
5.4 ± 5.2
8.2 ± 6.8
8.1 ± 14.1
4.6 ± 3.5
v6 (13°); v20 (11°)
v1 (14°); v20 (11°)
v1 (35°)
v1 (31°); v6 (11°)
v1 (15°)
v20 (23°); v1, v30 & v3, (14–17°)
v20 (22°); v30 , v3, v1 & v40 (12–16°)
Evenly distributed (2–9°)
v20 , v2 (17–18°); v30 , v40 , v60 , v3 (12°)
v20 & v2 (10–12°)
v1 (13°)
v1 (25°); v60 (21°)
All but the x, v1 & v6, rest 15–20°
Evenly distributed (9–20°)
v20 & v2 (17°)
x (13°); x’ & v1 (10°)
v60 (23°); v20 , x’ & x (12–14°)
v20 , v2 (17–20°); v30 , v40 , v60 , v3 (12°)
x (14°), rest evenly distributed (1–7°)
v1 (30°), v3, v6 & v40 (13–16°)
v1 (13°)
v20 , v30 , v3 & v40 (11–15°)
v6 & x (12–19°)
Evenly distributed (2–8°)
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.
vs MM3 (e = 4)
vs MM3 (e = 1.5)
MAD
RRD
MAD
1.76
1.06
1.06
1.35
0.89
1.99
2.59
1.16
0.92
0.96
0.40
1.54
1.59
2.43
1.58
3.04
3.57
0.73
2.72
2.25
2.08
2.73
1.99
1.61
8.36
4.13
4.98
8.81
3.51
7.83
10.4
4.58
4.28
5.32
1.72
8.97
7.43
7.43
7.03
9.26
6.65
4.07
7.79
9.95
5.95
8.63
8.99
5.92
RRD
1.35
2.12
4.77
7.32
1.98
2.24
2.12
2.36
8.97
7.64
10.5
10.0
1.47
2.32
3.58
1.79
6.94
9.77
7.71
9.31
2.50
2.09
9.60
10.3
2.75
11.1
1.48
2.18
1.88
6.31
4.50
3.37
vs Amber94
MAD
RRD
1.53
4.58
0.85
0.64
2.20
1.44
2.45
1.41
2.36
2.90
0.39
3.32
2.99
1.51
3.21
2.56
2.44
2.35
2.95
11.2
5.87
5.97
6.68
9.17
10.2
1.46
8.36
13.5
5.19
12.1
10.3
8.68
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
3.3. a-Galabiose
a-Galabiose has received less attention than the previous disaccharides. However, there are some published adiabatic maps in the
literature.30,59 Again, two minima are found in the main area. Both
are close in energy with MM3 at e = 80, and have a 20° separation
in the / torsion angle. The displacement is almost 60° in the w torsion angle,59 which means a better separation than is observed for
b-cellobiose. These minima were also named A and B.59 The current survey also used 27 starting structures in the A minimum
and 27 in the B (Fig. 2). The analysis of the minima produced by
each force field (Table 1) shows that with most methods, the minima in the A and B regions are quite stable. With GLYCAM at e = 4,
about half of the A structures shifted to B, whereas CHARMM19
shifted a similar proportion from B to A (Table 1). The remaining
force fields retained most starting geometries in their original
form, and only a few were not able to keep some of the original
structures. Figure 6 shows the /,w regions for the A and B minima
calculated with each force field. Table 5 compares the torsion angles of the remaining exocyclics and indicates which of the 54 conformers is the global minimum within each calculation. It also
gives the statistical comparison of the force fields with the ‘reference models’. Figure 6 shows that the only force field that gives
odd locations for the minima is CHARMM27. The remaining force field
results fit more or less with each other, especially in the B region,
which shows very little deviation among different force fields. In
the A region, the other CHARMM variants (19 and 22) are only slightly
apart, and GLYCAM06 (e = 1) is within the same region, but with a
2225
large standard deviation. The only crystal structure found for the
present compound72 has /,w of 98°, 158°, and its hydroxymethyl
groups are disordered. In the major form most structures are gtgt,
but in the minor form they are tgtg. The crystal structure falls in the
A minimum, at values close to those found by most force fields. The
match is usually better with calculations made at e = 4, and the
best matches are with MM2, MM4, and OPLS-2005, although others (such as GROMOS, MM3, GLYCAM06, or the semiempirical
PM3CARB-1) have very close geometrical data (Fig. 6).
Regarding the exocyclics (Table 5), the force fields closest to
MM3 (e = 4) are MM+, Amber3, Amber99, GLYCAM06, GROMOS,
and OPLS-2005 at e = 4. The main exocyclic change is for v1 (Table
5). This angle, influenced by the exoanomeric effect, is about 50°
in MM3 and most of the other force fields, but MM2 and GLYCAM
lead it to a value up to 90°, as occurred (with reversed sign) with
the b-anomer of cellobiose. PM3CARB-1 also shows large differences, especially regarding v2 and v3.
About half of the methods (Table 5) gave A as the preferred
minimum energy region, and the other half gave B. A tendency
to stabilize the B region was observed when the dielectric constant
was lowered. This extra stabilization changes the global minimum
from the A to the B region when lowering the dielectric constant
with OPLS-2005 and GLYCAM06 (Table 5). The stability of the B
conformer was also increased by 0.9–2 kcal/mol with MM3,
MM4, and GROMOS, but not enough to make it the global minimum. CSFF shows a more erratic behavior. The hydroxymethyl
groups of the global minima appear to be in the gg, gt, or tg orientation, 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
MM3 (e = 1.5)
MMX (e = 4)
Tinker MM2 (e = 4)
Tinker MM2 (e = 1.5)
MM+ (e = 1.5)
MM4 (e = 4)
MM4 (e = 1.5)
Amber3
Amber94
Amber99
GLYCAM06 (e = 4)
GLYCAM06 (e = 1)
CHARMM 19
CHARMM 22
CHARMM 27
CSFF (e = 4)
CSFF (e = 1)
OPLS original
OPLS 05 (e = 4)
OPLS 05 (e = 1)
GROMOS (e = 4)
GROMOS (e = 1)
PM3CARB-1
A, gtgg
B, gtgt
A, gggg
A, gggg
B, gtgt
A, gggg
A, gggg
A, gtgg
B, gtgt
B, gtgt
B, gtgt
A, gtgg
B, gttg
B, gttg
A, tggt
B, gtgt
B, ggtg
B, gtgt
B, tggt
A, gtgg
A, gggg
A, gggg
A, gggg
Average difference of
the 10 exocyclic torsionals (°)
Most affected torsionals (average)
7.4 ± 9.9
8.6 ± 6.7
9.5 ± 13.0
11.2 ± 14.4
4.8 ± 6.3
8.6 ± 7.8
9.3 ± 7.5
5.7 ± 6.2
11.3 ± 9.0
8.0 ± 6.4
5.3 ± 7.2
11.2 ± 13.0
12.7 ± 9.1
10.1 ± 8.5
9.8 ± 9.0
8.0 ± 8.4
10.8 ± 16.0
12.3 ± 9.6
5.2 ± 5.1
12.8 ± 24.5
5.3 ± 5.4
8.5 ± 11.0
12.3 ± 20.7
v60 , v2 & v3 (10–12°)
v1 & v20 (13°); v60 , v2 & v3 (10°)
v1 (33°); v6 (17°)
v1 (35°); v6 (15°)
v1 (14°)
v1 (17°); v6, v30 , v3 & v40 (10–13°)
v6, v30 , v3, v1 & v40 (11–15°)
v20 , v1 & v2 (10–12°)
v20 , v2 (18–23°); v30 , v40 , v60 , v3 (13°)
(16°); v1 & v2 (10–12°)
v1 & v20 (11–13°)
v1 (25°); v20 , v2 & v3 (12–16°)
All but the x & v1, rest 12–22°
v20 & v2 (18–22°); v60 & v30 (12°)
v20 & v2 (17–24°); v60 & v30 (12°)
v20 , x0 , x & v1 (10–13°)
All but x’, rest 9–15°
v20 , v2 (20–24°); v30 , v40 , v60 , v3 (14°)
Evenly distributed (1–10°)
v1 (42°), v3, v30 , v2, v6, v40 (10–16°)
v1 (12°)
v3 (19°) v20 & v30 (11–12°)
v2, v3 (24–28°); v60 , v6, v30 (12–15°)
vs MM3 (e = 4)
vs MM3 (e = 1.5)
MAD
RRD
MAD
RRD
3.06
2.02
1.09
1.43
1.75
2.23
4.05
1.39
2.48
1.01
0.98
2.77
3.21
3.68
2.10
1.99
2.84
2.99
3.48
4.99
0.94
3.23
2.07
7.70
4.40
4.16
5.94
2.83
7.51
11.1
2.56
4.77
3.22
3.53
8.45
5.53
10.4
7.67
5.79
15.2
6.09
9.18
10.1
4.52
11.9
12.6
2.30
4.79
5.42
10.39
1.27
4.44
5.49
3.95
6.70
8.75
12.3
9.08
1.42
5.97
6.74
4.81
8.31
12.7
17.9
12.1
2.96
6.03
16.2
13.8
2.50
9.15
1.82
2.41
8.56
8.78
vs Amber94
MAD
RRD
1.45
5.34
1.59
1.74
5.02
1.36
1.68
1.80
0.94
4.50
0.59
1.90
7.27
2.56
5.34
3.87
3.34
3.78
11.3
5.18
6.93
8.34
3.81
14.1
2.10
10.9
14.6
7.76
15.9
13.5
Units of MAD and RRD are kcal/mol.
MAD and RRD, the force fields that show the best energy coincidence (Table 5) with MM3 (e = 4) are GLYCAM06 and GROMOS
(at e = 4), and Amber99. The best energy coincidences with MM3
at e = 1.5 are also given by GLYCAM06 and GROMOS, this time
working at e = 1, and also by MM4.
3.4. New force fields
The current results show that the newer force fields or parameterizations, such as GROMOS, GLYCAM06, CSFF, MM4 and OPLS2005 behave with greater similarity than the older ones, with the
exception of MM3. These results are based on comparisons of energies and geometries with crystal and DFT data. In most cases, the
results obtained by Amber and CHARMM variants (as well as the
old OPLS) in HyperChem are more divergent than those produced
by MM3 and the newer force fields. The MM2 variants usually give
intermediate results. In order to avoid the use of a single reference
method (at least at first), a benchmark comparison of the six force
fields was made, working at e = 4 and separately working at e = 1
(1.5 for MM3 and MM4). The exocyclic angle differences, MAD
and RRD are shown in Table 6 as an average of the results for the
three disaccharides. Working at e = 4, similar geometries appear
for MM3, GLYCAM06, GROMOS, and OPLS (the closest is between
GLYCAM and GROMOS). On the other hand, MM4 gives the worst
coincidence. At e = 1/1.5, the coincidence is less, but the best overlap is between MM3 and GROMOS (Table 6). Regarding the energies, 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
the worst agreement with any other force field, whereas CSFF and
MM4 give intermediate values. Also, at e = 1/1.5 the best coincidences are seen between MM3, MM4, GLYCAM, and GROMOS,
whereas OPLS and especially CSFF results are rather different (Table 6). These results indicate that when working with GLYCAM06,
GROMOS, or MM3 the results can be compared favorably, as they
appear to be more homogeneous than those that arise from working with other force fields.
Table 6
Cross tables showing the differences in exocyclic torsionals, MAD and RRD between
six selected force fields, at both high (4) and low (1 or 1.5) dielectric constantsa
MM3
Difference between the
MM3
—
MM4
6.8
GLYCAM06
7.4
OPLS 2005
8.2
CSFF
7.2
GROMOS
5.8
MM4
GLYCAM06
OPLS 2005
10 exocyclic torsional angles (°)
10.0
4.9
4.8
—
11.9
12.1
11.5
—
4.9
8.3
10.1
—
9.4
7.8
7.9
7.0
8.4
7.7
CSFF
GROMOS
7.6
14.1
8.5
7.4
—
7.2
5.0
12.4
3.0
5.2
8.5
—
MAD (kcal/mol)
MM3
—
MM4
1.44
GLYCAM06
1.57
OPLS 2005
2.28
CSFF
3.08
GROMOS
1.41
1.66
—
1.94
2.07
3.23
1.67
0.58
1.95
—
2.56
2.60
1.90
2.65
3.74
2.74
—
4.42
3.01
2.16
3.30
1.77
3.66
—
2.91
1.50
2.05
1.58
3.84
1.37
—
RRD (kcal/mol)
MM3
—
MM4
6.36
GLYCAM06
6.53
OPLS 2005
9.04
CSFF
12.43
GROMOS
6.55
6.32
—
8.65
9.97
12.26
8.14
2.32
5.64
—
8.48
9.37
7.11
7.89
10.00
7.89
—
12.50
10.45
7.39
12.01
6.53
12.82
—
12.44
5.52
8.16
4.85
11.52
5.35
—
The results are averages of those obtained for b-cellobiose, a-maltose, and agalabiose.
a
The boldface numbers correspond to calculations at e = 1 or 1.5, whereas the
normal font is used for values calculated at e = 4.
4. Conclusions
The current search of disaccharide conformers indicates that
most of the force fields were able to find minima in all the low-energy regions, and that only a few of them were driven to other minima. Amber94 and the original OPLS force field give similar results
for disaccharide conformers. The variants of CHARMM give very poor
agreement, odd /,w angles for minima, and difficulties in finding
some minima.
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
The experimental values available support the results of many
different force fields. However, crystal data agree better with the
calculations made at e = 4 than with those made at lower dielectric
constants, whereas the latter match better with DFT results. The
newer force fields (GROMOS, GLYCAM06, OPLS-2005 and CSFF)
agree better with experiment and DFT results than older Amber,
CHARMM or OPLS versions. Thus, new studies with those older force
fields should be discouraged. However, it is surprising to find that
an older general-purpose force field like MM3 gives results comparable to those of the newer ones (although it appears to be less
dielectric constant dependent). The newer force fields look better
than those of MM2 variants (which are still acceptable) and are
comparable to those of MM4. PM3CARB-1 also shows more than
acceptable results on these calculations. Although the present calculations did not otherwise involve quantum mechanics calculations, the newer force fields benefit extensively from QM, as their
parameterizations are based on mimicking QM results. Thus, newer parameterizations typically take advantage of higher levels of
quantum theory, with the hope of getting better results.
The current results showed that MM3 can serve well as a reference method. The results in /,w space obtained from the other
methods surrounded the MM3 results. Also, the MAD and RRD energy values computed by pairing MM3 with each of the other force
fields were lower than pairings based on any other force field.
Using it at e = 4, the following conclusions on the comparative
behavior of other methods can be found:
The /,w values that match better with the reference are those
generated by other Allinger force fields. MM3 at e = 1.5 is usually
the closest. PM3CARB-1 and the newer force fields also give
quite similar results. The CHARMM variants give the largest difference compared to the reference method.
When comparing the exocyclic angles, the following five methods show the best agreement with the reference for the three
disaccharides: OPLS-2005 (e = 4), GLYCAM06 (e = 4), GROMOS
(e = 4), Amber3, and MM+, followed by MM3 (e = 1.5) and
Amber99. CHARMM variants and the original OPLS tend to give larger deviations.
The best agreement with the reference energies is given by GLYCAM06 at e = 4. The three Amber variants, MM2 (at e = 4), GROMOS and the original OPLS also give acceptable agreements. The
CHARMM variants, MM4, and OPLS-2005 results deviate considerably from the reference, although this is dependent upon the
disaccharide under study.
The various Allinger force fields (e.g., MM2, MM3, and MM4)
show good agreement with each other for a given e value (4 or
1.5). The Amber type force fields even at e = 1 show good agreement with MM3 at higher dielectric constants, suggesting that
these force fields are parameterized to simulate condensed
phases.
MM3, GLYCAM06, and GROMOS appear to be the best choices to
study disaccharides. MM4, CSFF, and OPLS-2005 are good alternatives. OPLS-2005 gives geometries comparable to MM3, but different relative energy values. Among the three top choices,
GLYCAM06 has shown a tendency to minimize conformers further
in a higher energy /,w region towards the lower energy one, probably due to a low-energy barrier set between the regions. Thus,
some higher energy conformers are overlooked with this method.
In any case, the geometries and energies of the resulting conformers match those of the best methods.
The present results still show substantial variations based on
each particular force field, just as differences result from different
levels of QM theory. Some of this variation could be due to the use
of explicit solvation during the development of the parameters, as
discussed in Introduction. The full-time modeler will always want
2227
to take advantage of the latest developments in force field parameterization, bearing in mind that the job of force field developers is
to continue improving previous systems. For those who have other
main interests, however, it is of importance to find a convergence
of results for a number of force fields, including some that are
available in easy-to-implement, relatively inexpensive software
systems. These programs may lack many of the features of the
packages that are used by specialists but make fewer demands
on the researcher.
Acknowledgments
This work was supported by grants from UBA and CONICET
(C.A.S.), and normal research funds from the Agricultural Research
Service of the U.S. Department of Agriculture (A.D.F. and G.P.J.).
C.A.S. is a Research Member of the National Research Council of
Argentina (CONICET).
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
Pérez, S. Curr. Opin. Struct. Biol. 1993, 3, 675–680.
Thøgersen, H.; Lemieux, R. U.; Bock, K.; Meyer, B. Can. J. Chem. 1982, 60, 44–57.
Tvaroška, I.; Pérez, S. Carbohydr. Res. 1986, 149, 389–410.
Csonka, G. I.; French, A. D.; Johnson, G. P.; Stortz, C. A. J. Chem. Theor. Comput.
2009, 5, 679–692.
(a) French, A. D.; Brady, J. W. ACS Symp. Ser. 1990, 430, 1–19; (b) Stortz, C. A.
Carbohydr. Res. 1999, 322, 77–86.
Melberg, S.; Rasmussen, K. Carbohydr. Res. 1979, 69, 27–38.
Melberg, S.; Rasmussen, K. Carbohydr. Res. 1979, 71, 25–34.
Melberg, S.; Rasmussen, K. Carbohydr. Res. 1980, 78, 215–224.
(a) French, A. D. Biopolymers 1988, 27, 1519–1523; (b) French, A. D. Carbohydr.
Res. 1989, 188, 206–211.
(a) Ha, S. N.; Madsen, L. J.; Brady, J. W. Biopolymers 1988, 27, 1927–1952; (b)
Tran, V.; Bulèon, A.; Imberty, A.; Pérez, S. Biopolymers 1989, 28, 679–690.
(a) Jiménez-Barbero, J.; Noble, O.; Pfeffer, C.; Pérez, S. New J. Chem. 1988, 12,
941–946; (b) Imberty, A.; Tran, V.; Pérez, S. J. Comput. Chem. 1990, 11, 205–216.
Melberg, S.; Rasmussen, K. J. Mol. Struct. 1979, 57, 215–239.
Allinger, N. L. J. Am. Chem. Soc. 1977, 99, 8127–8134.
Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.;
Karplus, M. J. Comput. Chem. 1983, 4, 187–217.
Ha, S.; Giammona, A.; Field, M.; Brady, J. W. Carbohydr. Res. 1988, 180, 207–221.
Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 8551–8567.
Dowd, M. K.; Zeng, J.; French, A. D.; Reilly, P. J. Carbohydr. Res. 1992, 230, 223–
244.
Dowd, M. K.; French, A. D.; Reilly, P. J. Carbohydr. Res. 1992, 233, 15–34.
(a) Dowd, M. K.; Reilly, P. J.; French, A. D. J. Comput. Chem. 1992, 13, 102–114;
(b) Dowd, M. K.; French, A. D.; Reilly, P. J. J. Carbohydr. Chem. 1995, 14, 589–
600; (c) Koča, J.; Pérez, S.; Imberty, A. J. Comput. Chem. 1995, 16, 296–310; (d)
Stortz, C. A.; Cerezo, A. S. J. Carbohydr. Chem. 1998, 17, 1405–1419; (e) Mazeau,
K.; Pérez, S. Carbohydr. Res. 1998, 311, 203–217; (f) Stortz, C. A. Carbohydr. Res.
2002, 337, 2311–2323.
Mendonca, S.; Johnson, G. P.; French, A. D.; Laine, R. A. J. Phys. Chem. A 2002,
106, 4115–4124.
Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J. 1987, 15,
197–210.
Weiner, S. J.; Kollman, P. A.; Case, D. A.; Singh, U. C.; Ghio, C.; Alagona, G.;
Profeta, S., Jr.; Weiner, P. J. Am. Chem. Soc. 1984, 106, 765–784.
Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. Soc. 1988, 110, 1657–1666.
(a) Senderowitz, H.; Parish, C.; Still, W. C. J. Am. Chem. Soc. 1996, 118, 2078–
2086; (b) Ott, K.-H.; Meyer, B. J. Comput. Chem. 1996, 17, 1068–1084.
(a) Glennon, T. M.; Zheng, Y.-J.; LeGrand, S. M.; Shutzberg, B. A.; Merz, K. M., Jr.
J. Comput. Chem. 1994, 15, 1019–1040; (b) Momany, F. A.; Willett, J. L.
Carbohydr. Res. 2000, 326, 194–209.
Woods, R. J.; Dwek, R. A.; Edge, C. J.; Fraser-Reid, B. J. Phys. Chem. 1995, 99,
3832–3846.
Kirschner, K. N.; Yongye, A. B.; Tschampel, S. M.; González-Outeriño, J.; Daniels,
C. R.; Foley, B. L.; Woods, R. J. J. Comput. Chem. 2008, 29, 622–655.
Lins, R. D.; Hünenberger, P. H. J. Comput. Chem. 2005, 26, 1400–1412.
Guvench, O.; Greene, S. N.; Kamath, G.; Brady, J. W.; Venable, R. M.; Pastor, R.
W., ; Mackerell, A. D., Jr. J. Comput. Chem. 2008, 29, 2543–2564.
French, A. D.; Kelterer, A.-M.; Johnson, G. P.; Dowd, M. K.; Cramer, C. J. J.
Comput. Chem. 2001, 22, 65–78.
French, A. D.; Kelterer, A.-M.; Cramer, C. J.; Johnson, G. P.; Dowd, M. K.
Carbohydr. Res. 2000, 326, 305–322.
(a) Csonka, G. I.; Sosa, C. P. J. Phys. Chem. A 2000, 104, 7113–7122; (b) Csonka, G.
I.; Sosa, C. P.; Csizmadia, I. G. J. Phys. Chem. A 2000, 104, 3381–3390.
Momany, F. A.; Willett, J. L. J. Comput. Chem. 2000, 21, 1204–1219.
Strati, G. L.; Willett, J. L.; Momany, F. A. Carbohydr. Res. 2002, 337, 1833–1849.
Momany, F. A.; Schnupf, U.; Willett, J. L.; Bosma, W. B. Struct. Chem. 2007, 18,
611–632.
2228
C. A. Stortz et al. / Carbohydrate Research 344 (2009) 2217–2228
36. French, A. D.; Johnson, G. P. Cellulose 2004, 11, 449–462.
37. (a) da Silva, C. O.; Nascimento, M. A. C. Carbohydr. Res. 2004, 339, 113–122; (b)
French, A. D.; Johnson, G. P.; Kelterer, A.-M.; Csonka, G. I. Tetrahedron:
Asymmetry 2005, 16, 577–586; (c) Schnupf, U.; Willett, J. L.; Bosma, W.;
Momany, F. A. Carbohydr. Res. 2007, 342, 2270–2285; (d) Schnupf, U.; Willett, J.
L.; Bosma, W.; Momany, F. A. J. Comput. Chem. 2008, 29, 1103–1112; (e)
Schnupf, U.; Willett, J. L.; Bosma, W.; Momany, F. A. Carbohydr. Res. 2009, 344,
362–373.
38. French, A. D.; Johnson, G. P. Can. J. Chem. 2006, 84, 603–612.
39. Gould, I. R.; Bettley, H. A.-A.; Bryce, R. A. J. Comput. Chem. 2007, 28, 1965–1973.
40. Pérez, S.; Imberty, A.; Engelsen, S. B.; Gruza, J.; Mazeau, K.; Jiménez-Barbero, J.;
Poveda, A.; Espinosa, J.-F.; van Eyck, B. P.; Johnson, G.; French, A. D.; Kouwijzer,
M. L. C. E.; Grootenuis, P. D. J.; Bernardi, A.; Raimondi, L.; Senderowitz, H.;
Durier, V.; Vergoten, G.; Rasmussen, K. Carbohydr. Res. 1998, 314, 141–155.
41. (a) Mackerell, A. D., Jr. J. Comput. Chem. 2004, 25, 1584–1604; (b) Hemmingsen,
L.; Madsen, D. E.; Esbensen, A. L.; Olsen, L.; Engelsen, S. B. Carbohydr. Res. 2004,
339, 937–948.
42. (a) Csonka, G. I.; Éliás, K.; Csizmadia, I. G. Chem. Phys. Lett. 1996, 257, 49–60; (b)
Csonka, G. I.; Éliás, K.; Kolossvary, I.; Sosa, C. P.; Csizmadia, I. G. J. Phys. Chem. A
1998, 102, 1219–1229; (c) Csonka, G. I.; Kolossváry, I.; Császár, P.; Éliás, K.;
Csizmadia, I. G. J. Mol. Struct. (THEOCHEM) 1997, 395/396, 29–40.
43. Barrows, S. E.; Storer, J. W.; Cramer, C. J.; French, A. D.; Truhlar, D. G. J. Comput.
Chem. 1998, 19, 1111–1129.
44. (a) Barrows, S. E.; Dulles, F. J.; Cramer, C. J.; French, A. D.; Truhlar, D. G.
Carbohydr. Res. 1995, 276, 219–251; (b) Stortz, C. A. An. Asoc. Quim. Argent.
1998, 86, 94–103; (c) Csonka, G. I.; Angyán, J. G. J. Mol. Struct. (THEOCHEM)
1997, 393, 31–38.
45. McNamara, J. P.; Muslim, A.-M.; Abdel-Aal, H.; Wang, H.; Mohr, M.; Hillier, I.
H.; Bryce, R. A. Chem. Phys. Lett. 2004, 394, 429–436.
46. Stortz, C. A. J. Comput. Chem. 2005, 26, 471–483.
47. Ponder, J. W. Tinker Software Tools for Molecular Design. Version 4.2, 2004
(http://dasher.wustl.edu/tinker).
48. Hyperchem for Windows 8.0; Hypercube, Inc., 2007.
49. Allinger, N. L.; Chen, K.-H.; Lii, J.-H.; Durkin, K. J. Comput. Chem. 2003, 24, 1447–
1472.
50. Lii, J.-H.; Allinger, N. L. J. Phys. Chem. A 2008, 112, 11903–11913.
51. Schrodinger, Portland, Oregon, www.schrodinger.com.
52. Kaminski, G. A.; Friesner, R. A.; Tirado-Rives, J.; Jorgensen, W. J. J. Phys. Chem. B
2001, 105, 6474–6487.
53. Case, D. A.; Darden, T. A.; Cheatham, T. E.; Simmerling, C. L.; Wang, J.; Duke, R.
E.; Luo, R.; Crowley, M.; Walker, R. C.; Zhang, W.; Merz, K. M.; Wang, B.; Hayik,
S.; Roitberg, A.; Seabra, G. ; Kolossváry, I.; Wong, K. F.; Paesani, F.; Vanicek, J.;
Wu, X.; Brozell, S. R.; Steinbrecher, T.; Gohlke, H.; Yang, V.; Tan, C.; Mongan, J.;
Hornak, V.; Cui, G.; Mathews, D. H.; Seetin, M. G.; Sagui, C.; Babin, V.; Kollman,
P. A., AMBER 10, University of California: San Francisco, 2008.
54. Kuttel, M.; Brady, J. W.; Naidoo, K. J. J. Comput. Chem. 2002, 23, 1236–1243.
55. (a) Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. Comp. Phys. Commun.
1995, 91, 43–56; (b) Lindahl, E.; Hess, B.; van der Spoel, D. J. Mol. Model. 2001, 7,
306–317; (c) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. J. Chem. Theor.
Comput. 2008, 4, 435–447.
56. van Gunsteren, W. F.; Billeter, S. R.; Eising, A. A. ; Hünenberger, P. H.; Krüger, P.;
Mark, A. E.; Scott, W. R. P.; Tironi, I. G. Biomolecular Simulation: The GROMOS96
Manual and User Guide. Vdf Hochschulverlag AG an der ETH Zürich, Zürich,
Switzerland, 1996; pp 1–1042.
57. Oostenbrink, C.; Soares, T. A.; van der Vegt, N. F. A.; van Gusteren, W. F. Eur.
Biophys. J. 2005, 34, 273–284.
58. Stortz, C. A.; Cerezo, A. S. Carbohydr. Res. 2003, 338, 95–107.
59. Stortz, C. A. Carbohydr. Res. 2006, 341, 663–671.
60. Strati, G. L.; Willett, J. L.; Momany, F. A. Carbohydr. Res. 2002, 337, 1851–1859.
61. (a) Chu, S. S. C.; Jeffrey, G. A. Acta Crystallogr., Sect. B 1968, 24, 830–838; (b)
Kalenius, E.; Kekäläinen, T.; Neitola, R.; Beyeh, K.; Rissanen, K.; Vainiotalo, P.
Chem. Eur. J. 2008, 14, 5220–5228.
62. (a) Ham, J. T.; Williams, D. G. Acta Crystallogr., Sect. B 1970, 26, 1373–1383; (b)
Leung, F.; Chanzy, H. D.; Pérez, S.; Marchessault, R. H. Can. J. Chem. 1976, 54,
1365–1371; (c) Raymond, S.; Henrisat, B.; Qui, D. T.; Kvick, Å.; Chanzy, H.
Carbohydr. Res. 1995, 277, 209–229; (d) Gessler, K.; Krauss, N.; Steiner, T.;
Betzel, C.; Sarko, A.; Saenger, W. J. Am. Chem. Soc. 1995, 117, 11397–11406; (e)
Bruhn, C.; Arendt, Y.; Steinboim, D. Z. Kristallogr. New Cryst. Struct. 2001, 216,
587–588; (f) Peralta-Inga, Z.; Johnson, G. P.; Dowd, M. K.; French, A. D.;
Rendleman, J. A.; Stevens, E. D.; French, A. D. Carbohydr. Res. 2002, 337, 851–
861; (g) Rencurosi, A.; Röhrling, J.; Pauli, J.; Potthast, A.; Jager, C.; Pérez, S.;
Kosma, P.; Imberty, A. Angew. Chem., Int. Ed. 2002, 41, 4277–4281.
63. Pérez, S.; Brisse, F. Acta Crystallogr., Sect. B 1977, 33, 2578–2584.
64. Yoneda, Y.; Mereiter, K.; Jaeger, C.; Brecker, L.; Kosma, P.; Rosenau, T.; French,
A. J. Am. Chem. Soc. 2008, 130, 16678–16690.
65. Nishiyama, Y.; Langan, P.; Chanzy, H. J. Am. Chem. Soc. 2002, 124, 9074–9082.
66. French, A. D.; Johnson, G. P. Mol. Simul. 2008, 34, 365–372.
67. Takusagawa, F.; Jacobson, R. A. Acta Crystallogr., Sect. B 1978, 34, 213–218.
68. (a) Chu, S. S. C.; Jeffrey, G. A. Acta Crystallogr. 1967, 23, 1038–1049; (b) Gress, M.
E.; Jeffrey, G. A. Acta Crystallogr., Sect. B 1977, 33, 2490–2495.
69. (a) Brisse, F.; Marchessault, R. H.; Pérez, S.; Zugenmaier, P. J. Am. Chem. Soc.
1982, 104, 7470–7476; (b) Köll, P.; Petrušova, M.; Petruš, L.; Zimmer, B.; Morf,
M.; Kopf, J. Carbohydr. Res. 1993, 248, 37–43.
70. Johnson, G. P.; Stevens, E. D.; French, A. D. Carbohydr. Res. 2007, 342, 1210–
1222.
71. (a) Tanaka, I.; Tanaka, N.; Ashida, T.; Kakudo, M. Acta Crystallogr., Sect. B 1976,
32, 155–160; (b) Pangborn, W.; Langs, D.; Pérez, S. Int. J. Biol. Macromol. 1985, 7,
363–369; (c) Schouten, A.; Kanters, J. A.; Kroon, J.; Looten, P.; Duflot, P.;
Mathlouthi, M. Carbohydr. Res. 1999, 322, 274–278.
72. Svensson, G.; Albertsson, J.; Svensson, C.; Magnusson, G.; Dahmén, J. Carbohydr.
Res. 1986, 146, 29–38.