Ramachandran-Type Plots for Glycosidic Linkages:
Examples from Molecular Dynamic Simulations Using the
Glycam06 Force Field
AMANDA M. SALISBURG, ASHLEY L. DELINE, KATRINA W. LEXA, GEORGE C. SHIELDS,* KARL N. KIRSCHNERy
Chemistry Department, Center for Molecular Design, Hamilton College Clinton, New York 13323
Received 24 January 2008; Revised 26 May 2008; Accepted 8 July 2008
DOI 10.1002/jcc.21099
Published online 10 September 2008 in Wiley InterScience (www.interscience.wiley.com).
Abstract: The goals of this article are to (1) provide further validation of the Glycam06 force field, specifically
for its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Ramachandran’s idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formed
between carbohydrates. As in traditional Ramachandran plots, these carbohydrate Ramachandran-type (carb-Rama)
plots reveal the coupling between the glycosidic angles by displaying the allowed and disallowed conformational
space. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be defined
by (a, /, w) and (b, /, w), whereas for three-bond linkages, there are 54 possible regions that can be defined by (a,
/, w, x) and (b, /, w, x). Illustrating these ideas are molecular dynamic simulations on an implicitly hydrated oligosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare and
contrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06
force field through comparison to experimental data, and discuss the general trends observed in the plots.
q 2008 Wiley Periodicals, Inc.
J Comput Chem 30: 910–921, 2009
Key words: Glycam force field; carbohydrate; Ramachandran plot; molecular dynamics; disaccharide
Introduction
Recently, the Glycam06 force field was published, which was
specifically designed to model carbohydrates but whose utility
can be extended to other compound classes.1 This force field
was validated by comparing gas-phase molecular mechanics
results to quantum mechanical gas-phase data, and by comparing
explicitly hydrated molecular dynamics simulations to a number
of different condensed-phase experimental data. Herein we perform several simulations using an implicit water model and
compare the obtained conformers and their distribution to those
found by X-ray and NMR methods. To aid our discussion and
description of the obtained conformers, we discuss and elaborate
on how Ramachandran plots can be extended to carbohydrates.
In 1963, G.N. Ramachandran introduced the idea of plotting
the phi angle versus the psi angle for amino acid peptide linkages to reveal the coupling between these two angles.2,3 Recognizing that an amino acid’s backbone can define a plane, Ramachandran was able to define the relative orientation of two adjacent amino acids by these two degrees of freedom. This greatly
reduced the number of terms required for defining the occupied
conformational space of peptide linkages, resulting in the easily
interpretable and very popular two-dimensional plots. These
plots are well understood, with specific regions of allowed and
disallowed conformational areas displayed.
Ramachandran’s idea can be extended to di-, poly-, and oligosaccharides. Analogous to amino acids, the representation of a
carbohydrate can be reduced to a plane that is formed by four
ring atoms (see Fig. 1). In general, a carbohydrate’s ring puckering does not change (e.g., 4C1 for pyranoside), allowing the
relative orientation between two adjoined carbohydrates to be
defined by the angles between the planes, which can be
described by the glycosidic angles phi (/) and psi (w). An addiAdditional Supporting Information may be found in the online version of
this article.
*Present address: Dean, College of Science and Technology, Armstrong
Atlantic State University, Savannah, Georgia 31419
y
Present address: Fraunhofer Institute for Algorithms and Scientific
Computing, Department of Simulation Engineering, Schloss Birlinghoven
53754 Sankt Augustin, Germany and is a guest at the Max Plank Institute for Molecular Physiology, OttoHahnStr. 11, D44227 Dortmund,
Germany.
Correspondence to: G.C. Shields; e-mail: George.Shields@armstrong.
edu or K. N. Kirschner; e-mail: [email protected]
Contract/grant sponsor: National Institutes of Health; contract/grant number: 1RI5CA11552401
Contract/grant sponsor: NSF; contract/grant numbers: CHE0457275,
CHE0116435, and CHE0521053 as part of the MERCURY high
performance computer consortium (http://mercury.chem.hamilton.edu)
q 2008 Wiley Periodicals, Inc.
Molecular Dynamic Simulations Using the Glycam06 Force Field
Figure 1. Graphical representation of the planes formed by carbohydrates, and the phi (/), psi (w), and omega (x) angles that can be
used to provide the relative orientation of the two planes.
tional angle, omega (x), is required for 1?6 linkages. The
coupling between these angles can be observed by plotting phi
versus psi versus omega. As in traditional Ramachandran plots,
these carbohydrate Ramachandran-type (carb-Rama) plots display allowed and disallowed conformational space.
Unique to carbohydrates are the number of possible linkages
that can be formed between carbohydrate residues. Amino acids
and DNA form polymeric chains in a single manner regardless of
the residue involved; carbohydrates can form several different
glycosidic linkages that depend on (a) the position in the ring
(e.g., 1?1, 1?3, 1?6), (b) the form of the anomeric center of
the nonreducing carbohydrate forming the linkage, axial (a) or
equatorial (b), and (c) the glycosidic linkage position, axial or
equatorial, that is formed on the reducing carbohydrate.4 The later
two factors depend on the individual carbohydrate (e.g., glucose,
mannose, galactose). For example, a-D-Glc-(1?2)-b-D-Man will
have a set of phi and psi values that may differ from those present
in b-D-Glc-(1?2)-b-D-Glc. Finally, the conformations adopted by
glycosidic linkages are influenced by the surrounding environment, such as solvent molecules or an attached protein.5,6
911
The structure–activity relationship paradigm is a widely
accepted and useful theory in biochemical and medicinal
research. Understanding the properties and function of biomolecules relies partially on understanding their three-dimensional
geometry. Significant effort has gone into understanding the
amino acid code and the nucleic acid code and how they relate
to function and geometry, as in the protein-folding problem.
Studying the sugar code permits us to recognize the allowed and
disallowed three-dimensional geometries of glycosidic linkages.
Although there are numerous examples in the literature of
carb-Rama plots created for specific linkages, including the
formation of potential surface maps (a.k.a. conformational
maps) using a particular level of theory,7–18 NMR-NOE based
maps,19–22 and MD scatter plots,23–27 there has been little effort
at creating generalized carb-Rama plots. In 1999 and 2002, Wormald and coworkers surveyed available NMR and X-ray data of
oligosaccharides and glycopeptides. In this work, they presented
carb-Rama plots based on experimental data.22,28 Experimental
data provide the foundation for the development of allowed and
disallowed conformational space of glycosidic linkages. However, much of this data involves large glycans attached to a protein because there is little experimental data for unbound
oligosaccharides or disaccharides. Recently, Frank and coworkers
have published an online database that provides free energy carbRama maps derived from MD simulations.29,30 These simulations
were performed using the MM3 force field modified for Tinker
at a temperature of 1000 K and with the carbohydrate rings
constrained, and it is unclear if they included solvent in their calculation. This database includes links to experimentally
determined (crystallographic and NMR) phi, psi, and omega
angle values. A similar online database has been developed by
the Centre National de la Recherche Scientifique and is called
Glyco3D. Thus, the concept of assigning Ramachandran-type
maps to carbohydrate linkages is an issue that is becoming more
popular.
In this article, we report the results of a 700 ns unrestrained
MD simulation performed at a temperature of 300 K on an implicitly hydrated oligosaccharide composed of 12 carbohydrate
residues, shown in Figure 2. We have also performed 50 ns MD
simulations on the eight constituent disaccharides that compose
this oligosaccharide. The objective of this article is threefold:
(1) we will present solution-phase carb-Rama plots for each of
the eight disaccharides, as well as compare and discuss how
they are different from the plots formed by the oligosaccharide;
(2) we will validate our modeling, and the Glycam06 force field,
by comparing the simulation results to experimental X-ray and
NMR data; and (3) we will discuss general trends in the carbRama plots. The simulation results and the carb-Rama plots will
be useful for future oligosaccharide studies in determining the
Figure 2. The oligosaccharide studied in this article. The disaccharides studied are composed from
this oligosaccharide, each having significant X-ray and NMR experimental data available for comparison and validation of simulations.
Journal of Computational Chemistry
DOI 10.1002/jcc
912
Salisburg et al. • Vol. 30, No. 6 • Journal of Computational Chemistry
Figure 3. (a, b) Phi, psi, and omega carb-Rama plots for the disaccharide’s glycosidic linkages.
factors that cause specific glycosidic linkage conformations to
be adopted (i.e., intrinsic to the linkage type itself or due to
external forces arising from the environment).
Methods
All minimizations and MD calculations were performed using
the AMBER 8 and 9 software packages using the GLYCAM06
force field.1 Nonbonded and electrostatic scaling factors were set
to unity, consistent with the development of GLYCAM06. Initial
geometries were optimized through 5000 cycles of steepest
descent, followed by conjugate gradient energy minimization
until the convergence criteria of drms ¼ 0.1 was obtained. MD
simulations were carried out in implicit solvent using Hawkins,
Cramer, and Truhlar’s generalized Born model, with default
AMBER radii.31,32 Each system was then heated from 5 to
300 K in 50 ps. Initial velocities were assigned from a Boltz-
mann distribution at 5 K. A 2-fs time step was used to integrate
the equations of motion. Temperatures were maintained at 300
K using a weak-coupling algorithm.33 A cutoff of 100 Å was
used for nonbonded interactions, thus calculating all nonbonded
pairs. Bonds containing hydrogen were constrained to their equilibrium lengths using the SHAKE algorithm.34 Subsequently,
force evaluations were computed with bond interactions involving the hydrogen atoms omitted. Families were determined
through the use and comparison of phi, psi, and omega histograms, which were generated using 58 bins.
Results
The Ramachandran-type plots resulting from the disaccharides
and oligosaccharide MD simulations are shown in Figures 3 and
4. The figures in the supplementary material display the /-, w-,
and x-angles as a function of simulation time for all systems
Journal of Computational Chemistry
DOI 10.1002/jcc
Molecular Dynamic Simulations Using the Glycam06 Force Field
Figure 4. (a–c) Phi, psi, and omega carb-Rama plots for the oligosaccharide glycosidic linkages.
Journal of Computational Chemistry
DOI 10.1002/jcc
913
Journal of Computational Chemistry
89.5
121.8
119.8
121.5
90.7
171.7
2179.9
291.5
83.8
2178.9
87.2
274.8
272.3
2123.5
273.9
276.2
272.9
2109.2
276.7
285.9
(b,2sc,þsc|ap)
(b,2sc,2sc)
(b,þsc,ap)
(b,ap,þsc)
(b,2sc,þsc|ap)
(b,2sc|ap,þsc)
1?6
(a,2sc,ap,gg)
(a,2sc,ap,gt)
(a,2sc,2sc,gt)
(a,2sc,þsc,gg)
(a,2sc,ap,tg)
(a,2sc,þsc,gt)
124.3
2121.1
52.6
268.7
2107.2
(b,2sc|ap,þsc)
(b,þsc,þsc|ap)
(b,2sc,2sc)
(b,2sc,þsc|ap)
(a,ap,2sc)
(a,þsc,þsc)
1?4
79.0
2143.7
289.7
50.4
2123.4
53.6
284.7
(b,2sc|ap,ap)
(b,þsc,2sc)
(b,2sc,þsc)
1?3
(a,þsc,2sc)
283.2
Psi
273.6
Phi
(b,2sc,2sc)
1?2
Linkage
270.0
74.8
79.3
277.2
154.4
67.2
Omega
Disaccharides
DOI 10.1002/jcc
63
19
5
5
4
4
80
20
100
30
\1
69
100
4
1
\1
94
%
Psi
Omega
287.1
284.9
274.4
2106.3
278.4
278.4
6
\1
94
\1
\1
100/99
%
a-L-Fuc-(1?6)-b-D-GlcNAc
169.2
280.5
178.7
71.9
2100.8
87.2
85.6
280.7
2168.6
164.5
94.5
68.8
87
3
4
4
2
\1
59
41
98
1
\1
\1
44/12
2/1
11/3
b-D-Gal-(1?4)-b-D-GlcNac
122.2/124.7
43/84
271.0
90.3
a-D-Man-(1?3)-b-D-Man
2119.6
289.0
54.2
2110.6/ 2136.9
90.4/88.3
55.5/52.2
119.0/123.0
287.4/267.1
264.9/250.5
b-D-GlcNac(1?4)-b-D-GlcNAc
276.3
116.9
264.3
253.1
66.2
135.4
2169.9
60.6
b-D-Man-(1?4)-b-D-GlcNac
270.0
123.4
2135.7
94.3
274.9/271.0
155.9
95.9
79.4
58.1
283.1
b-D-GlcNAc-(1?2)-a-D-Man
293.0/278.3
287.7/286.1
Phi
12-Mera
Table 1. Disaccharides Average Phi, Psi, and Omega Angles Obtained from MD Simulations.
10.9
5
4
10
275 6 13.7
286.5 6 10.8
275 6 11.6
271.4 6
296 6
275 6
287 6
274
275
71.5 6 8.8
75 615
80 6 15
80
100
58.3 6 9.4
280.1 6 12.6
292 6 16
280
Phi
7.4
3
4
11
2155.1 6 24.0
110.7 6 19.4
119 6 15.4
132.2 6
154 6
138 6
146 6
138
139
2120.6 6 16.8
2135 6 15
2116 6 25
2130
290
287.2 6 15.2
297.6 6 22.3
283 6 14
290
Psi
Omega
256.6 6 12.3
Experimental
24 X-ray22
197 X-ray22
376 X-ray22
28 X-ray22
NMR21,36
130 X-ray22
NMR7,19,35
8 X-ray22
53 X-ray22
NMR35
#
914
Salisburg et al. • Vol. 30, No. 6 • Journal of Computational Chemistry
8 NMR37–40,42–44
(averaged)
14 X-ray22
29 X-ray22
38 X-ray22
29 X-ray22
NMR35
Population percentages are given for each conformation.
When two values are present, the first value comes from the 1?6 branch, whereas the second value come from the 1?3 branch.
2125.1 þ 15.5
68.5 6 13.6
10/8
2143.2/2145.8
7
2140.5
39.5
(a,þsc,ap)
45.7/42.6
90/92
a-D-NeuAc-(2?3)-b-D-Gal
2140.5/2143.1
93
2142.5
236.7
(a,2sc,ap)
1
89.4
276.5
96.3
236.0/236.3
2
\1
1
53.3
95.3
269.4
61.0
74.8
99.2
53.3
86.6
97.7
94.4
14
3
273.3
159.0
(a,þsc,þsc,gg)
(a,þsc,ap,tg)
(a,þsc,þsc,gt)
(a,þsc,þsc,gt)
(a,þsc,2sc,gt)
2?3
80.7
77.4
95.3
2178.1
81.4
267.0
91
59.4 6 7.5
243.5 6 14.8
94.0 6 17.5
2139.3 6 17.8
68.5 6 12.3
260.3 6 14.0
66.0 6 12.8
60.6 6 20
2178.4 6 10.0
178.5 6 13.7
2170 6 20
5
\1
67
15
177.8
2173.4
78.5
75.0
(a,þsc,ap,gg)
(a,þsc,ap,gt)
271.3
72.2
81.2
65.4
a-D-Man-(1?6)-b-D-Man
169.5
269.3
167.6
69.7
64.7 6 10.4
67.0 6 10.5
70 6 20
Omega
%
Omega
Psi
%
Omega
Psi
Phi
Linkage
Table 1. (Continued)
Disaccharides
Phi
12-Mera
Phi
Psi
Experimental
#
Molecular Dynamic Simulations Using the Glycam06 Force Field
915
reported and include the histograms for each angle. Table 1
reports the average /-, w-, and x-angles for the families populated about each glycosidic linkage within the disaccharides and
the oligosaccharide. We have adopted the following glycosidic
angle
definitions:
/
¼
O50 #
#C10 #
#Ox#
#Cx,
w
¼
C10 #
#Ox#
#Cx#
#Cx21, and x ¼ O6#
#C6#
#C5#
#O5 for all 1?n
linkages, whereas for the 2?3 linkage / ¼ O60 #
#C20 #
#O3#
#C3
and w ¼ C20 #
#O3#
#C3#
#C2.
The a-L-Fuc-(1?6)-b-D-GlcNAc-OMe disaccharide populates
six different families, with 63% of the population clustered
around the average angle values of 2748 (/), 1728 (w), and
2708 (x), and 19% clustered around 2768 (/), 1808 (w), and
758 (x). The remaining four families have 5% or less population. Experimentally, this linkage possesses average values of
275.78 6 13.78 (/), 2155.18 6 24.08 (w), and 256.68 6 12.38
(x), as determined from 24 crystal structures,*,22 corresponding
to the most populated MD family. The same families are populated in the oligosaccharide, with 87% of the population clustered
around 2878 (/), 1698, (w) and 2808 (x). The remaining fiveoligosaccharide families have 5% or less population.
The b-D-GlcNAc-(1?4)-b-D-GlcNAc-OMe disaccharide populates a single conformation that is clustered around 2758 (/) and
1208 (w). This corresponds very well to the average experimental
values of 275 6 11.68(/) and 119 6 15.48(w), obtained from 376
crystal structures that posses this linkage.y,22 The same family is seen
in the oligosaccharide, clustered around 2768(/) and 1178(w).
The b-D-Man-(1?4)-b-D-GlcNAc-OMe disaccharide populates two families with 80% of the population clustered around
2728(/) and 1228(w), with the remaining 20% clustered around
21248(/) and 918 (w). An average of 197 crystal structures
found this linkage to have average values of 286.58 6 10.88(/)
and 110.78 6 19.48(w),22 corresponding to the most populated
MD family. Both families are seen in the oligosaccharide, with
59% of the population clustered around 2708(/) and 1238 (w)
and 41% clustered around 21368(/) and 948(w).
The a-D-Man-(1?6)-b-D-Man-OMe disaccharide populates
five families, with 67% clustered around 788(/), 1788(w), and
2718(x), 15% clustered around 758(/), 21738(w), and 728(x),
14% clustered around 818(/), 958(w), and 2738(x), and the
remaining families have less than 5% occupancy. Crystallographic studies have clearly seen two families populating this
linkage. An average of 38 crystal structures found values of 64.7
6 10.48(/), 2178.4 6 10.08(w), and 260.3 6 14.08(x),22 corresponding to the most populated MD family. An average of 29
crystal structures found angles of 67.0 6 10.58(/), 178.5 6
13.78(w), and 66.0 6 12.88(x),22 corresponding closely to the
second most populated MD family. NMR spectroscopy on this
linkage found values of 70 6 208(/) and 2170 6 208(/) and
60.6 6 208(x), also corresponding to the second most populated
MD family.35 The oligosaccharide MD simulation significantly
*Note that the omega angle in ref. 22 was defined as O6#
#C6#
#C5#
#O4,
and required the addition of 1208 to convert it to the O6#
#C6#
#C5#
#O5
definition used here.
y
This particular disaccharide underwent a ring flip during the simulation.
The system was resimulated with igb ¼ 5, resulting in a stable 4C1 ring.
Thus, for the remainder of the article the results computed with igb ¼ 5
will be used.
Journal of Computational Chemistry
DOI 10.1002/jcc
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Salisburg et al. • Vol. 30, No. 6 • Journal of Computational Chemistry
populates two of these families, with 91% clustered around
818(/), 948(w), and 2678(x), and 5% clustered around 818(/),
1708(w), and 2698(x). The remaining two families are populated by less than 5%. Interestingly, one of these families is not
seen in the disaccharides but is seen experimentally, with an
average angle (29 crystal structures) of 59.4 6 7.58(/), 94.0 6
17.58(w), and 68.5 6 12.38(x).22
The a-D-Man-(1?3)-b-D-Man-OMe disaccharide populates a
single family clustered around 798(/) and 21078(w) for the
entire simulation. This corresponds well with the experimental
average values of 71.5 6 8.88(/) and 2120.6 6 16.88(w)
obtained from 130 crystal structures,22 as well as NMR values
of 75 6 158(/) and 2135 6 158(w), 808(/) and 21308(w),
1008(/) and 2908(w), and 80 6 15(/) and 2116 6
25(w).35,7,19 Nearly the same conformation is populated in the
oligosaccharide simulation, with 94% clustered around 798(/)
and 21208(w), and a new family that is clustered around
1568(/) and 2718(w) with 6% population.
The b-D-GlcNAc-(1?2)-a-D-Man-OMe disaccharide populates four families during the MD simulation, with 94% clustered around 2748(/) and 2838(w), and the remaining three
families having less than 5% occupancy. The major family corresponds well to the experimentally averaged values of 280.1 6
12.68(/) and 297.6 6 22.38(w), obtained from 53 crystal structures.22 NMR experiments have determined /- and w-values of
2808(/) and 2908(w), and 292 6 168(/) and 283 6
148(w),35 both corresponding to the most populated MD family.
A second experimental family is seen, with average angles of
58.3 6 9.48(/) and 287.2 6 15.28(w) as determined over eight
crystal structures.22 This family is observed in the disaccharide
simulation with a population of 1%, whose angles have an average value of 548(/) and 2908(w). The b-D-GlcNAc-(1 ? 2)-aD-Man linkage is present twice in the oligosaccharide, each clustered around 2938(/) and 2888(w) (1?6 branch) and 2788(/)
and 2868(w) (1?3 branch) for 100% of the simulation.
The b-D-Gal-(1?4)-b-D-GlcNAc-OMe disaccharide populates
three families during the MD simulation, with 69% clustered
around 2698(/) and 1248(w), 30% clustered around 21218 (/)
and 908(w), and less than 1% clustered around 538(/) and
1228(w). An average of 28 crystal structures found average angles
of 271.4 6 10.98(/) and 132.2 6 7.48(w),22 corresponding to the
most populated MD family. In agreement with these findings are
five NMR whose //w values include 296 6 5/154 6 3, 275 6
4/138 6 4, 287 6 10/146 6 11, 274/138, and 275/139.21,36
The two most populated families are also observed in both
branches of the oligosaccharide. The 1?6 branch possesses 43%
of the population clustered around 2758(/) and 1228(w), whereas
the 1?3 branch possesses 84% of the population clustered around
2718(/) and 1258(w). For the second family the 1?6 branch possesses 44% of the population clustered around 21118(/) and
908(w), whereas the 1?3 branch possesses 12% of the population
clustered around 21378(/) and 888(w). A third family is populated in the oligosaccharide, one that is not seen in the disaccharides, with a population of 11% clustered around 2878(/) and
2658(w) in the 1?6 branch and 3% clustered around 2678(/)
and 2508(w) in the 1?3 branch.
Finally, the a-D-NeuAc-(2?3)-b-D-Gal-OMe disaccharide
populates two families during the MD simulation, with 93% clus-
tered around 2378(/) and 21428(w), whereas the remaining family is clustered around 408(/) and 21408(w). In terms of a-DNeuAc-(2?n) linkages, the 2?3 linkage has the most available
NMR6,21,37–43 and X-ray experimental data.22 The NMR studies
are coupled with computations to provide values for the /- and
w-angles that are consistent with the NMR spectra. Eight NMR
values yielded a /- and w-values of 243.58 6 14.88 and 2139.38
6 17.88,37–40,42–44 corresponding to the most populated MD conformation. One NMR study yielded a values of 358 and 21088,43
whose /-value corresponds to the less populated MD family. An
average of 14 crystal structures found angles of 68.58 6 13.68 (/)
and 2 125.18 6 15.58 (w),22 which is questionably populated by
the disaccharide MD simulation at 7%. The oligosaccharide simulation populates the same two families seen in the disaccharide.
The most abundant family has a population of 90% (1?6 branch)
and 92% (1?3 branch) clustered around 2368(/) and 21428(w).
The second family has 10% and 8% clustered around 448(/) and
21448(w) in the 1?6 and 1?3 branches, respectively.
Discussion
Conformational Space of Carb-Rama Plots for Ideal
Linkage Angles
Recently, da Silva and coworkers presented a nice discussion of
the anomeric and exo-anomeric effect in carbohydrates.45 The
anomeric effect refers to the thermodynamic preference for the
axial (a) position of electronegative groups (e.g., methoxy or
carbohydrate) over the beta (b) position at the anomeric C1
atom. Quantifying this is the angle C50 #
#O50 #
#C10 #
#Ox (h),
where a has a h-angle of 608 and b has a y-angle of 1808.{ The
exo-anomeric effect refers to the preference for conformations
about the /-angle. The /-angle may adopt conformations centered around 2608 (2sc, synclinal or gauche), 608 (þsc), and
1808 (ap, antiperiplaner or trans).45,46 Considering only the hand /-angles for two-bond glycosidic linkages (e.g., 1?2, 1?3,
2?3. . .), the relative order in increasing stability, based on QM
calculations on 2-methoxytetrahydropyran, is (a, þsc), (b, 2sc),
(a, ap), (b, þsc), (b, ap), and (a, 2sc).45,46 Including the wangle results in 18 possible conformations defined by (a, /, w)
and (b, /, w).§ Including the x-angle for the 1?6 glycosidic
linkage results in 54 possible conformations defined by (a, /, w,
x) and (b, /, w, x), whose ideal angles are presented in Table
2. The common nomenclature for the x-angle is gauche–trans
(gt), trans–gauche (tg), and gauche–gauche (gg), referring to the
x-angle and O6#
#C6#
#C5#
#C4, respectively. The gt, tg, and gg
conformations have x-angle values of approximately 608, 1808,
and 2608, respectively. As a nomenclature example, (a, þsc,
2sc, gt) indicates a conformation about an a 1?6 linkage that
possesses a positive gauche /-angle, a negative gauche w-angle
and a gt x-angle. Based on these ideal angles, the carb-Rama
plot for any two-bond a-linkages, will have nine regions of
{
The exception to this is a-D-NeuAc-, where the a conformation possesses a y-angle of 1808 as defined by C60 #
#O60 #
#C2#
#Ox.
§
A similar type of conformational analysis uses a diamond-lattice to
describe the conformational space of glycosidic linkages, and interested
readers are referred to refs. 47 and 48 for further information.
Journal of Computational Chemistry
DOI 10.1002/jcc
Molecular Dynamic Simulations Using the Glycam06 Force Field
917
a
Table 2. Nomenclature and ideal torsion angles for the 18 and 54 possible conformations for two-and
three-bond glycosidic linkages, respectively.
y
y
/
w
Two-bond glycosidic linkage (e.g. 1?2,1?3, 1?4)
(a,þsc,þsc)
60
60
60
(a,ap,þsc)
(a,þsc,2sc)
60
60
260
(a,ap,2sc)
(a,þsc, ap)
60
60
180
(a,ap,ap)
(a,2sc,þsc)
60
260
60
(b,þsc,þsc)
(a,2sc,2sc)
60
260
260
(b,þsc,2sc)
(a,2sc,ap)
60
260
180
(b,þsc,ap)
60
60
60
180
180
180
180
180
180
60
60
60
60
260
180
60
260
180
Three-bond glycosidic linkage (e.g. 1?6)
(a,þsc,þsc,gt)
60
60
60
(a,þsc,þsc,gg)
60
60
60
(a,þsc,þsc,tg)
60
60
60
(a,þsc,2sc,gt)
60
60
260
(a,þsc,2sc,gg)
60
60
260
(a,þsc,2sc,tg)
60
60
260
(a,þsc, ap,gt)
60
60
180
(a,þsc,ap,gg)
60
60
180
(a,þsc,ap,tg)
60
60
180
(a,2sc,þsc,gt)
60
260
60
(a,2sc,þsc,gg)
60
260
60
(a,2sc,þsc,tg)
60
260
60
(a,2sc,2sc,gt)
60
260
260
(a,2sc,2sc,gg)
60
260
260
(a,2sc,sc,tg)
60
260
260
(a,2sc,ap,gt)
60
260
180
(a,2sc,ap,gg)
60
260
180
(a,2sc,ap,tg)
60
260
180
60
60
60
60
60
60
60
60
60
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
60
60
60
60
60
60
60
60
60
60
60
60
260
260
260
180
180
180
60
60
60
260
260
260
180
180
180
/
w
x
60
260
180
60
260
180
60
260
180
60
260
180
60
260
180
60
260
180
(a,ap,þsc,gt)
(a,ap,þsc,gg)
(a,ap,þsc,tg)
(a,ap,2sc,gt)
(a,ap,2sc,gg)
(a,ap,2sc,tg)
(a,ap,ap,gt)
(a,ap,ap,gg)
(a,ap,ap,tg)
(b,þscþsc,gt)
(b,þsc,þsc,gg)
(b,þsc,þsc,tg)
(b,þsc,2sc,gt)
(b,þsc,2sc,gg)
(b.þsc,2sc,tg)
(b,þsc,ap,gt)
(b,þsc,ap,gg)
(b,þsc,ap,tg)
y
/
w
(b,2sc,þsc)
(b,2sc,2sc)
(b,2sc,ap)
(b,ap,þsc)
(b,ap,2sc)
(b,ap,ap)
180
180
180
180
180
180
260
260
260
180
180
180
60
260
180
60
260
180
(b,2sc,þsc,gt)
(b,2sc,þsc,gg)
(b,2sc,þsc,tg)
(b,2sc,2sc,gt)
(b,2sc,2sc,gg)
(b,2sc,2sc,tg)
(b,2sc,ap,gt)
(b,2sc,ap,gg)
(b,2sc,ap,tg)
(b,ap,þsc,gt)
(b,ap,þsc,gg)
(b,ap,þsc,tg)
(b,ap,2sc,gt)
(b,ap,2sc,gg)
(b,ap,2sc,tg)
(b,ap,ap,gt)
(b, ap,ap,gg)
(b,ap,ap,tg)
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
260
260
260
260
260
260
260
260
260
180
180
180
180
180
180
180
180
180
60
60
60
260
260
260
180
180
180
60
60
60
260
260
260
180
180
180
x
60
260
180
60
260
180
60
260
180
60
260
180
60
260
180
60
260
180
x
60
260
180
60
260
180
60
260
180
60
260
180
60
260
180
60
260
180
a
Two-bond glycosidic linkages are defined by (a, /, w) and (b, /, w), and three-bond glycosidic linkages are defined
#O05#
#C01#
#Ox; / ¼ O05#
#C01#
#Ox#
#Cx; w ¼
by (a, /,w,x) and (b, /,w,x). Torsion definitions: a/b ¼ C05#
0
C#
#Ox#
#Cx#
#Cx-1; x ¼ O6#
# C6#
#C5#
#O5. The abbreviations 2sc,þsc and ap refer to an angle adopting a value
that is 2608 (negative synclinal or gauche), þ608 (positive synclinal or gauche) and 1808 (antiperiplaner or trans),
respectively. The abbreviations gt, tg and gg refer to gauche-trans, trans-gauche, and gauche-gauche in reference in
the x angle and O6#
#C6#
#C5#
#C4, respectively.
possible conformational space, with each region enclosed by a
1208 3 1208 (w 3 /) area as shown in Supplementary Figure 1.
The same will be true for the carb-Rama plots for any two-bond
b-linkages. The three-dimensional carb-Rama plots for any
three-bond a- or b-linkage (e.g., 1?6, 2?6) will have 27
regions of possible conformational space, each enclosed by a
1208 3 1208 3 1208 (w 3 / 3 x) volume. However, not all of
the conformational regions may be accessible due to energetic
restraints, while other regions may be preferentially populated.
Finally, in the situations where angles adopt a value that borders two regions, we will indicate this by a ‘‘|’’ in the conformation nomenclature. For example if an MD simulation samples
conformations that possess /-angles in the þsc and ap regions,
but all of the conformations belong to a single / family, the
family would be indicated by (b, þsc, þsc|ap). The angles that
fall into this category have angle values that are 1208 6 58 or
21208 6 58.
Linkage Conformations from Simulations and Experiment
The carb-Rama plots for b-D-GlcNAc-(1?2)-a-D-Man show that
the major family populated by the disaccharide and the oligosac-
charide is (b, 2sc, 2sc). In the oligosaccharide this linkage
behaves similarly in the 1?3 and 1?6 branches. The 1?6
branch linkage has the average /-angle shifted by approximately
2178, whereas the w-angle resembles that of the disaccharide
and the 1?3 branch. This shift can be explained by the 1?6
linkage forming multiple contacts with the inner carbohydrates,
exemplified in Figure 5a, which induces the shift in its average
angle adopted. The disaccharide also has a (b, 2sc|ap, ap) conformation that is populated for 4% of the simulation time. The
remaining two conformational families are (b, þsc, 2sc) and (b,
2sc, þsc), both having very low populations (i.e., $1%).
The carb-Rama plots for the b-D-GlcNAc-(1?4)-b-D-GlcNAc
linkage are very similar for both the disaccharide and the oligosaccharide, adopting essentially 100% of the (b, 2sc, þsc|ap)
conformation. Replacing the terminal b-D-GlcNac with b-D-Man,
forming b-D-Man-(1?4)-b-D-GlcNAc, opens a nearby (b,
2sc|ap, þsc) conformational space, while retaining (b, 2sc,
þsc|ap) as the most abundant family in the disaccharide and oligosaccharide simulations. Interestingly, the carb-Rama plots for
the b-D-Man-(1?4)-b-D-GlcNAc linkage shows a 21% population shift between the disaccharide and oligosaccharide simulations. The most abundant family is populated 80% of the time in
Journal of Computational Chemistry
DOI 10.1002/jcc
918
Salisburg et al. • Vol. 30, No. 6 • Journal of Computational Chemistry
Figure 5. The representations of three oligosaccharide conformations that were sampled during the
MD simulations, labeled A, B, and C. The blue residues are the carbohydrates belonging to the 1 ? 6
branch, the red represent the carbohydrates on the 1 ? 3 branch, and the traditionally colored residues
are the inner core of the oligosaccharides.
the disaccharide, which reduces to 59% in the oligosaccharide.
Concurrently, the new and second most abundant family goes
from a 20% population in the disaccharide to 41% population in
the oligosaccharide. The increase in the oligosaccharide’s (b,
2sc|ap, þsc) family is due to the 1?6 branch interacting with
the inner core carbohydrates, such that the 1?6 branch lies
behind the fucose residue Figure 5b.
The other 1?4 linkage, b-D-Gal-(1?4)-b-D-GlcNAc, displays similar traits to those mentioned above, with (b, 2sc,
þsc|ap) being the most abundant family and (b, 2sc|ap, þsc)
being the second most abundant family. As in the b-D-Man(1?4)-b-D-GlcNAc linkage, there is a shift that occurs between
these families. The b-D-Gal-(1?4)-b-D-GlcNAc linkage present
in the oligosaccharide’s 1?6 branch accesses a new conformation, (b, 2sc, 2sc), for 11% of the simulation time, which is in
addition to the equally populated (b, 2sc, þsc|ap) and (b,
2sc|ap, þsc) families at %44%. This is not the case in the 1?3
branch, where the (b, 2sc,þsc|ap) family increases in population
by 15% relative to the disaccharide. The populated (b, 2sc|ap,
þsc) and (b, 2sc, 2sc) families have significantly reduced occupancy of 12% and 3%, respectively.
The a-D-Man-(1?3)-b-D-Man linkage has the (a, þsc, 2sc)
family populated for 100% of the disaccharide simulation, and
94% of the oligosaccharide simulation. The oligosaccharide possesses an additional conformation, (a, ap, 2sc), with a 6% population. This new conformation occurs when the 1?3 branch
wraps back to interact with the inner core carbohydrates, forming a stacked topology as exemplified in Figure 5c.
The carb-Rama plots for a-D-NeuAc-(2?3)-b-D-Gal indicate
that the (a, 2sc, ap) conformation is the most dominate family
in both simulations, with 93% population in the disaccharide,
and 90% and 92% in the 1?6 and 1?3 oligosaccharide
branches, respectively. This family is seen in nearly all NMR
studies. The less populated MD family is (a, þsc, ap), with
10% or less occupancy, which is not seen experimentally. However, the closely related family, (a, þsc, 2sc|ap), is seen in
X-ray experiments. Of the residues studied here, a-D-NeuAcproved the most challenging to parameterize due to its potential
to be ionized in solution and the number of mixed functionalities that govern the /-angle torsion.1 These results suggest that a
revisit of the a-D-NeuAc parameterization might be warranted.
In all simulations involving the 1?6 linkage, the x-angle
predominately samples the gt and gg conformations, with a
sampling of less than 4% for the tg conformation. The lack of
the tg conformation is understood based on the ‘‘repulsive’’ xangle curve, which will be qualitatively similar to the repulsive
curve presented for a-D-glucopyranoside that we presented previously.49 This curve is characterized by minima at gt and gg,
whereas none exist around tg due to a repulsive interaction
between the O6 and the O4 atoms. As explained previously,49
electrostatic and steric repulsions are the underlying factors in
determining the x-angle’s gt and gg preferences when the
carbohydrate’s hydrogen bonding is occupied by solvent interactions. For the disaccharides and oligosaccharides, these
forces dominate the behavior of x-angle even more because
the reducing carbohydrate’s O6 atom is unable to be a hydrogen bond donor, which would marginally stabilize the tg
conformation.
The carb-Rama plots for the a-L-Fuc-(1?6)-b-D-GlcNAc
linkage are similar between the disaccharides and the oligosaccharide, both primarily populating an (a, 2sc, þsc, gg) conformation. Five other families are populated, which include (a,
2sc, ap, gt), (a, 2sc, 2sc, gt), (a, 2sc, þsc, gg), (a, 2sc, ap,
tg), and (a, 2sc, þsc, gt). This linkage adopts a single /-angle
conformation that is 2sc in both simulations, consistent with the
exo-anomeric effect. The (a, 2sc, ap, gg) population occurs
with a /-angle near 21078, an approximately 2308 distortion
from the other families, and is directly coupled to the adoption
of a w-angle and an x-angle of 808 and 2808, respectively. In
this conformation, the /-angle distorts to avoid steric hinderence
between the #
#NHC(¼
¼O)H and the methyl group attached to
fucose’s C5 atom. The (a, 2sc, ap, tg) conformation (4%) occurs
when the x-angle is 1608 (tg), violating the gauche effect, and
occurs only when / and w adopt values around 2758 and
21708, respectively.
The largest a-L-Fuc-(1?6)-b-D-GlcNAc family, (a, 2sc, ap,
gg), shows a 24% population increase in the oligosaccharide at
the expense of (a, 2sc, ap, gt), the second largest disaccharide
family. The change in family preference is due to the x-angle
adopting a conformation that allows for more favorable contacts
with the 1?6 branch.
Journal of Computational Chemistry
DOI 10.1002/jcc
Molecular Dynamic Simulations Using the Glycam06 Force Field
The carb-Rama plots for a-D-Man-(1?6)-b-D-Man show a
significant shift in populations when comparing the disaccharides
with the oligosaccharide. The largest shift occurs with the (a,
þsc, ap, gg) conformation, which is the dominant conformation
in the disaccharide (67%) to the second most dominant conformation (5%) in the oligosaccharide. This corresponds to an
increase in the third most populated disaccharide conformation,
(a, þsc, þsc, gg) (14%), which becomes the most dominant
conformation (91%) in the oligosaccharide. Interestingly, the xangle preferentially adopts a gg conformation that is long lived
in the oligosaccharide, which is contrary to the frequent sampling observed in the disaccharide simulations. Thus, the addition of the 10 other carbohydrate residues stiffens the x-angle.
Comparison of MD Simulations to Experiment
The average /-, w-, and x-angles of major families in the MD
simulations correspond well with available experimental data.
The most populated family in each linkage is experimentally
observed in X-ray or NMR spectroscopy. By comparing the average MD value (Table 1) with the average X-ray values determined by Wormald and coworkers,22 the /-, w-, and x-angles are
modeled very well, with an average absolute difference from the
X-ray of 10.38, 12.68, and 14.08, respectively. The largest /-angle
difference occurs in the oligosaccharide for b-D-Man-(1?4)-b-DGlcNAc linkage’s (b, 2sc, þsc|ap) conformation and for a-DMan-(1?6)-b-D-Man linkage’s (b, þsc, ap, gg) conformation,
with an absolute difference of 16.58 and 16.38, respectively.
The largest w-angle difference, with respect to the average crystal values, occurs in the disaccharide and oligosaccharide a-L-Fuc(1?6)-b-D-GlcNAc linkage (a, 2sc, ap, gg) conformation, with
absolute values of 32.98 and 35.98, respectively. The third largest
w-angle difference occurs at an absolute value of 14.68 in the disaccharide b-D-GlcNAc-(1?2)-a-D-Man’s linkage. Additionally, the
a-D-NeuAc-(2?3)-b-D-Gal’s (a, 2sc, ap), when compared with the
average NMR values, has an absolute differences of less than 78.
The largest x-angle difference, with respect to the average
crystal values, occurs in the disaccharide and oligosaccharide
a-L-Fuc-(1?6)-b-D-GlcNAc linkage’s (a, 2sc, ap, gg) conformation, with absolute values of 13.48 and 23.48, respectively.
Likewise, the average MD values compare very well with available NMR data,7,19,21,35,36 with an average absolute difference
for /- and w-angles of 8.68 and 15.28, respectively. Only one
NMR determined x-angle is known, a-D-Man-(1?6)-b-D-Man’s
(b,þsc,ap,gg) linkage, and the disaccharide and oligosaccharide
simulations are within 11.48 and 9.48, respectively.
General Trends
b-D-(1?4)-equatorial: In this study, there are three different carbohydrate combinations that belong to this linkage type: b-DGlcNAc-(1?4)-b-D-GlcNAc, b-D-Man-(1?4)-b-D-GlcNAc, and
b-D-Gal-(1?4)-b-D-GlcNAc. The two significant conformations
that these b-(1?4)-equatorial linkages occupy in the simulations
are (b,2sc,þsc|ap) and (b,2sc|ap,þsc). The average of 376
crystal structures that possess a b-D-GlcNAc-(1?4)-D-GlcNAc
linkage yields average /- and w-angles of 275.98 6 11.68 and
119.08 6 15.48,22 respectively, placing them in the (b,2sc,þsc|ap)
919
region. The average of 28 crystal structures that possess a b-DGal-(1?4)-D-GlcNAc linkage yields average /- and w-angles of
2718 6 108 and 132.28 6 7.48,22 respectively, placing them in
the (b,2sc,ap) region. The average of 197 crystal structures that
possess a b- D-Man-(1 ? 4)-D-GlcNAc linkage yields average
/- and w-angles of 286.58 6 11.68 and 110.78 6 19.48,22 respectively, placing them in the (b,2sc,þsc) region. NMR spectroscopy on Lactose (b-D-Gal-(1?4)-b-D-Glc) and Cellobiose (b-DGlc-(1?4)-b-D-Glc) yields a /-angle of approximately 2878 and
a w-angle of approximately 998, placing these two linkages in the
(b,2sc,þsc) region.50,51 The average of two crystal structures that
possess b-D-GlcNAc-(1?4)-D-Man linkages provide average /and w-angles of 2170.08 6 10.78 and 94.78 6 6.18,22 respectively, placing them in the (b,ap,sc) region. This data taken together suggest that b-D-(1?4)-equatorial linkages preferentially
dominate the (b,2sc,þsc|ap) region, whereas the (b, sc|ap,þsc),
(b,2sc,ap), (b,2sc,2sc), and (b,ap,þsc) regions are accessible to
a lesser degree.
a-D-(1?3)-equatorial: The a-D-Man-(1?3)-b-D-Man linkage
preferentially populates the (a,þsc,2sc) region of the carb-Rama
plot. There are 130 crystal structures that possess an a-D-Man(1?3)-D-Man linkage whose average /- and w-angles are 71.58 6
8.88 and 2120.68 6 16.88,22 respectively, placing an average crystal
structure at (a,þsc,2sc|ap). In addition to this specific linkage, there
is NMR data available for Nigerose (a-D-Gal-(1?3)-b-D-Glc),
whose conformation is in the (a,þsc,ap) region with a /-angle of
818 and a w-angle of 21438.50 These values suggest a strong a-D(1?3)-equatorial linkage preference for the (a,þsc,2sc) and
(a,þsc,ap) regions.
a-D-(1?6)-equatorial: This linkage is the most difficult type
for which to provide general trends. The a-D-Man-(1?6)-b-DMan linkage populates three significant areas in the carb-Rama
plots, which are (a,þsc,ap,gg), (a,þsc,ap,gt), and (a,þsc,þsc,gg).
There are 96 crystal structures that possess an a-D-Man-(1?6)-DMan linkage occupying the regions (a,þsc,ap,gg), (a,þsc,ap,gt)
and (a,þsc,þsc,gt) whose average /-, w-, and x-angles in region
one are 64.78 6 10.48, 2178.48 6 10.08, and 260.38 6 14.08, in
region two are 67.08 6 10.58, 178.58 6 13.78, and 66.08 6 12.88,
and in region three are 59.48 6 7.58, 94.08 6 17.58, and 68.58 6
12.38,22 respectively. An NMR study on Melibiose (a-D-Man(1?6)-b-D-Man) found /- and w-angles of 76.88 and 21358.50
Based on the simulation results and the known experimental results,
the a-D-(1?6)-equatorial linkage preferentially populates the regions
(a,þsc,ap,gg), (a,þsc,ap,gt), (a,þsc,þsc,gg), and (a,þsc,þsc,gþ).
The MD simulations show that the a-L-Fuc-(1?6)-b-DGlcNAc linkage significantly populates the (a,2sc,ap,gg) and
(a,2sc,ap,gt) regions. Fucose posses an L configuration, which
causes the preferred /-angle conformation of þ608, as found in
the other a-D-(1?6)-equatorial linkages, to become 2608 for
this linkage. The three dimensional geometry of these regions is
similar for both the a-D-(1?6)-equatorial and a-L-(1?6)-equatorial, with a gauche conformation in the /-angle and a trans conformation in the C20 #
#C10 #
#O6#
#C6 torsion angle.
Conclusion
In this article, we present the extension of G.N. Ramachandran’s
idea of plotting the amino acid phi and psi angles to the glyco-
Journal of Computational Chemistry
DOI 10.1002/jcc
920
Salisburg et al. • Vol. 30, No. 6 • Journal of Computational Chemistry
sidic phi, psi and omega angles formed between carbohydrates.
Considering two-bond glycosidic linkages, there are 18 possible
conformational regions that can be defined by (a, /, w) and (b,
/, w), whereas for three-bond linkages there are 54 possible
regions that can be defined by (a, /, w, x) and (b, /, w, x).
We have reported the results of an implicitly hydrated molecular
dynamics simulation on an oligosaccharide composed of 12
carbohydrate residues, and on the eight constituent disaccharides
that compose this oligosaccharide.
The Glycam06 force field reproduces known experimental
data well, where the average /-, w-, and x-angles of major MD
conformational families correspond well with available experimental data. The most populated family for each linkage is
experimentally observed in X-ray or NMR spectroscopy. By
comparing the average MD values to the average X-ray values
determined by Wormald and coworkers,22 the /-, w- and xangles are modeled very well, with an average absolute difference from the X-ray values of 10.38, 12.68, and 14.08, respectively.
Three general trends can be seen in the carb-Rama plots and
experimental data. First, the b-(1?4)-equatorial linkages preferentially dominate the (b,2sc,þsc|ap) region, whereas the
(b,2sc|ap,þsc), (b,2sc,ap), (b,2sc,2sc), and (b,ap,þsc) regions
are accessible to a lesser degree. Second, a-(1?3)-equatorial
linkages show a strong preference for the (a,þsc,2sc) and
(a,þsc,ap) regions. Third, the a-D-(1?6)-equatorial linkages
preferentially populate the regions (a,þsc,ap,gg), (a,þsc,ap,gt),
and (a,þsc,þsc,gg).
The reported simulation results and the carb-Rama plots will
be useful for future oligosaccharide studies in determining the
factors that cause specific glycosidic linkage conformations to
be adopted. We hope that this presentation of carb-Rama plots
will aid others in unraveling the complex structure of di-, poly-,
and oligosaccharides.
Acknowledgments
Acknowledgment is made to NSF, NIH and to Hamilton College
for support of this work. This project was supported in part by
NIH grant, NSF grant, and by NSF Grants as part of the
MERCURY highperformance computer consortium (http://mercury.
chem.hamilton.edu).
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