Ramachandran-type plots for glycosidic linkages: Examples...

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 2008DOI 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, specificallyfor its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Rama-chandran’s idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formedbetween 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 conformationalspace. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be definedby (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 oli-gosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare andcontrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06force 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 wasspecifically designed to model carbohydrates but whose utilitycan be extended to other compound classes.1 This force fieldwas validated by comparing gas-phase molecular mechanicsresults to quantum mechanical gas-phase data, and by comparingexplicitly hydrated molecular dynamics simulations to a numberof different condensed-phase experimental data. Herein we per-form several simulations using an implicit water model andcompare the obtained conformers and their distribution to thosefound by X-ray and NMR methods. To aid our discussion anddescription of the obtained conformers, we discuss and elaborateon how Ramachandran plots can be extended to carbohydrates.

In 1963, G.N. Ramachandran introduced the idea of plottingthe phi angle versus the psi angle for amino acid peptide link-ages to reveal the coupling between these two angles.2,3 Recog-nizing that an amino acid’s backbone can define a plane, Rama-chandran was able to define the relative orientation of two adja-cent amino acids by these two degrees of freedom. This greatlyreduced the number of terms required for defining the occupiedconformational space of peptide linkages, resulting in the easilyinterpretable and very popular two-dimensional plots. Theseplots are well understood, with specific regions of allowed anddisallowed conformational areas displayed.

Ramachandran’s idea can be extended to di-, poly-, and oli-gosaccharides. Analogous to amino acids, the representation of acarbohydrate can be reduced to a plane that is formed by fourring atoms (see Fig. 1). In general, a carbohydrate’s ring pucker-ing does not change (e.g., 4C1 for pyranoside), allowing therelative orientation between two adjoined carbohydrates to bedefined by the angles between the planes, which can bedescribed by the glycosidic angles phi (/) and psi (w). An addi-

Additional 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 31419yPresent 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 Insti-tute 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 num-

ber: 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.

tional angle, omega (x), is required for 1?6 linkages. Thecoupling between these angles can be observed by plotting phiversus psi versus omega. As in traditional Ramachandran plots,these carbohydrate Ramachandran-type (carb-Rama) plots dis-play allowed and disallowed conformational space.

Unique to carbohydrates are the number of possible linkagesthat can be formed between carbohydrate residues. Amino acidsand DNA form polymeric chains in a single manner regardless ofthe residue involved; carbohydrates can form several differentglycosidic 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 ofthe nonreducing carbohydrate forming the linkage, axial (a) orequatorial (b), and (c) the glycosidic linkage position, axial orequatorial, that is formed on the reducing carbohydrate.4 The latertwo factors depend on the individual carbohydrate (e.g., glucose,mannose, galactose). For example, a-D-Glc-(1?2)-b-D-Man willhave a set of phi and psi values that may differ from those presentin b-D-Glc-(1?2)-b-D-Glc. Finally, the conformations adopted byglycosidic linkages are influenced by the surrounding environ-ment, such as solvent molecules or an attached protein.5,6

The structure–activity relationship paradigm is a widelyaccepted and useful theory in biochemical and medicinalresearch. Understanding the properties and function of biomole-cules relies partially on understanding their three-dimensionalgeometry. Significant effort has gone into understanding theamino acid code and the nucleic acid code and how they relateto function and geometry, as in the protein-folding problem.Studying the sugar code permits us to recognize the allowed anddisallowed three-dimensional geometries of glycosidic linkages.

Although there are numerous examples in the literature ofcarb-Rama plots created for specific linkages, including theformation of potential surface maps (a.k.a. conformationalmaps) using a particular level of theory,7–18 NMR-NOE basedmaps,19–22 and MD scatter plots,23–27 there has been little effortat creating generalized carb-Rama plots. In 1999 and 2002, Wor-mald and coworkers surveyed available NMR and X-ray data ofoligosaccharides and glycopeptides. In this work, they presentedcarb-Rama plots based on experimental data.22,28 Experimentaldata provide the foundation for the development of allowed anddisallowed conformational space of glycosidic linkages. How-ever, much of this data involves large glycans attached to a pro-tein because there is little experimental data for unboundoligosaccharides or disaccharides. Recently, Frank and coworkershave published an online database that provides free energy carb-Rama maps derived from MD simulations.29,30 These simulationswere performed using the MM3 force field modified for Tinkerat a temperature of 1000 K and with the carbohydrate ringsconstrained, and it is unclear if they included solvent in their cal-culation. This database includes links to experimentallydetermined (crystallographic and NMR) phi, psi, and omegaangle values. A similar online database has been developed bythe Centre National de la Recherche Scientifique and is calledGlyco3D. Thus, the concept of assigning Ramachandran-typemaps to carbohydrate linkages is an issue that is becoming morepopular.

In this article, we report the results of a 700 ns unrestrainedMD simulation performed at a temperature of 300 K on an im-plicitly hydrated oligosaccharide composed of 12 carbohydrateresidues, shown in Figure 2. We have also performed 50 ns MDsimulations on the eight constituent disaccharides that composethis oligosaccharide. The objective of this article is threefold:(1) we will present solution-phase carb-Rama plots for each ofthe eight disaccharides, as well as compare and discuss howthey 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 andNMR data; and (3) we will discuss general trends in the carb-Rama plots. The simulation results and the carb-Rama plots willbe useful for future oligosaccharide studies in determining the

Figure 1. Graphical representation of the planes formed by carbo-hydrates, and the phi (/), psi (w), and omega (x) angles that can beused to provide the relative orientation of the two planes.

Figure 2. The oligosaccharide studied in this article. The disaccharides studied are composed fromthis oligosaccharide, each having significant X-ray and NMR experimental data available for compari-son and validation of simulations.

911Molecular Dynamic Simulations Using the Glycam06 Force Field

Journal of Computational Chemistry DOI 10.1002/jcc

factors that cause specific glycosidic linkage conformations tobe adopted (i.e., intrinsic to the linkage type itself or due toexternal forces arising from the environment).

Methods

All minimizations and MD calculations were performed usingthe AMBER 8 and 9 software packages using the GLYCAM06force field.1 Nonbonded and electrostatic scaling factors were setto unity, consistent with the development of GLYCAM06. Initialgeometries were optimized through 5000 cycles of steepestdescent, followed by conjugate gradient energy minimizationuntil the convergence criteria of drms ! 0.1 was obtained. MDsimulations were carried out in implicit solvent using Hawkins,Cramer, and Truhlar’s generalized Born model, with defaultAMBER radii.31,32 Each system was then heated from 5 to300 K in 50 ps. Initial velocities were assigned from a Boltz-

mann distribution at 5 K. A 2-fs time step was used to integratethe equations of motion. Temperatures were maintained at 300K using a weak-coupling algorithm.33 A cutoff of 100 A wasused for nonbonded interactions, thus calculating all nonbondedpairs. Bonds containing hydrogen were constrained to their equi-librium lengths using the SHAKE algorithm.34 Subsequently,force evaluations were computed with bond interactions involv-ing the hydrogen atoms omitted. Families were determinedthrough the use and comparison of phi, psi, and omega histo-grams, which were generated using 58 bins.

Results

The Ramachandran-type plots resulting from the disaccharidesand oligosaccharide MD simulations are shown in Figures 3 and4. The figures in the supplementary material display the /-, w-,and x-angles as a function of simulation time for all systems

Figure 3. (a, b) Phi, psi, and omega carb-Rama plots for the disaccharide’s glycosidic linkages.

912 Salisburg et al. • Vol. 30, No. 6 • Journal of Computational Chemistry


Figure 4. (a–c) Phi, psi, and omega carb-Rama plots for the oligosaccharide glycosidic linkages.



Tab

le1.

Disaccharides

Average

Phi,Psi,andOmegaAng

lesObtainedfrom

MD

Sim

ulations.

Linkage

Disaccharides

12-M

era

Exp

erim

ental

Phi

Psi

Omega

%Phi

Psi

Omega

%Phi

Psi

Omega

#

1?2

b-D-G

lcNAc-(1?

2)-a-D-M

an

(b,2

sc,2

sc)

273

.6283

.294

293

.0/2

78.3

287

.7/2

86.1

100/99

280

.16

12.6

297

.66

22.3

53X-ray

22

292

616

283

614

NMR35

280

290

(b,2

sc|ap,ap)

212

3.4

214

3.7

4

(b,"

sc,2

sc)

53.6

289

.71

58.1

289

.0\1

58.3

69.4

287

.26

15.2

8X-ray

22

(b,2

sc,"

sc)

284

.750

.4\1

283

.154

.2\1

1?3

a-D-M

an-(1?

3)-b-D-M

an

(a,"

sc,2

sc)

79.0

210

7.2

100

79.4

211

9.6

9471

.56

8.8

212

0.66

16.8

130X-ray

22

75615

213

56

15NMR7,19,35

806

15211

66

25

80213

0

100

290

(a,ap,2sc)

155.9

271

.06

(a,"

sc,"

sc)

95.9

90.3

\1

1?4

b-D-G

al-(1?4)-b-D-G

lcNac

(b,2

sc,"

sc|ap)

268

.712

4.3

69274

.9/2

71.0

122.2/12

4.7

43/84

271

.46

10.9

132.26

7.4

28X-ray

22

296

65

1546

3NMR21,36

275

64

1386

4

287

610

1466

11

274

138

275

139

(b,2

sc|ap,"sc)

212

1.1

89.5

30211

0.6/

213

6.9

90.4/88.3

44/12

(b,"

sc,"

sc|ap)

52.6

121.8

\1

55.5/52.2

119.0/12

3.0

2/1

(b,2

sc,2

sc)

287

.4/2

67.1

264

.9/2

50.5

11/3

b-D-G

lcNac(1?4)-b-D-G

lcNAc

(b,2

sc,"

sc|ap)

274

.811

9.8

100

276

.311

6.9

98275

611

.611

96

15.4

376X-ray

22

(b,2

sc,2

sc)

264

.3253

.11

(b,"

sc,ap)

66.2

135.4

\1

(b,ap,"sc)

216

9.9

60.6

\1

b-D-M

an-(1?

4)-b-D-G

lcNac

(b,2

sc,"

sc|ap)

272

.312

1.5

80270

.012

3.4

59286

.56

10.8

110.76

19.4

197X-ray

22

(b,2

sc|ap,"sc)

212

3.5

90.7

20213

5.7

94.3

41

1?6

a-L-Fuc-(1?

6)-b-D-G

lcNAc

(a,2

sc,ap,gg)

273

.917

1.7

270

.063

287

.116

9.2

280

.587

275

613

.7215

5.16

24.0

256

.66

12.3

24X-ray

22

(a,2

sc,ap,gt)

276

.2217

9.9

74.8

19284

.917

8.7

71.9

3

(a,2

sc,2

sc,gt)

272

.9291

.579

.35

274

.4210

0.8

87.2

4

(a,2

sc,"

sc,gg)

210

9.2

83.8

277

.25

210

6.3

85.6

280

.74

(a,2

sc,ap,tg)

276

.7217

8.9

154.4

4278

.4216

8.6

164.5

2

(a,2

sc,"

sc,gt)

285

.987

.267

.24

278

.494

.568

.8\1



reported and include the histograms for each angle. Table 1reports the average /-, w-, and x-angles for the families popu-lated about each glycosidic linkage within the disaccharides andthe oligosaccharide. We have adopted the following glycosidicangle definitions: / ! O50##C10##Ox##Cx, w !C10##Ox##Cx##Cx21, and x ! O6##C6##C5##O5 for all 1?nlinkages, whereas for the 2?3 linkage / ! O60##C20##O3##C3

and w ! C20##O3##C3##C2.The a-L-Fuc-(1?6)-b-D-GlcNAc-OMe disaccharide populates

six different families, with 63% of the population clusteredaround the average angle values of 2748 (/), 1728 (w), and2708 (x), and 19% clustered around 2768 (/), 1808 (w), and758 (x). The remaining four families have 5% or less popula-tion. Experimentally, this linkage possesses average values of275.78 6 13.78 (/), 2155.18 6 24.08 (w), and 256.68 6 12.38(x), as determined from 24 crystal structures,*,22 correspondingto the most populated MD family. The same families are popu-lated in the oligosaccharide, with 87% of the population clusteredaround 2878 (/), 1698, (w) and 2808 (x). The remaining five-oligosaccharide families have 5% or less population.

The b-D-GlcNAc-(1?4)-b-D-GlcNAc-OMe disaccharide popu-lates a single conformation that is clustered around 2758 (/) and1208 (w). This corresponds very well to the average experimentalvalues of 275 6 11.68(/) and 119 6 15.48(w), obtained from 376crystal structures that posses this linkage.y,22 The same family is seenin the oligosaccharide, clustered around2768(/) and 1178(w).

The b-D-Man-(1?4)-b-D-GlcNAc-OMe disaccharide popu-lates two families with 80% of the population clustered around2728(/) and 1228(w), with the remaining 20% clustered around21248(/) and 918 (w). An average of 197 crystal structuresfound this linkage to have average values of 286.58 6 10.88(/)and 110.78 6 19.48(w),22 corresponding to the most populatedMD family. Both families are seen in the oligosaccharide, with59% 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 populatesfive families, with 67% clustered around 788(/), 1788(w), and2718(x), 15% clustered around 758(/), 21738(w), and 728(x),14% clustered around 818(/), 958(w), and 2738(x), and theremaining families have less than 5% occupancy. Crystallo-graphic studies have clearly seen two families populating thislinkage. An average of 38 crystal structures found values of 64.76 10.48(/), 2178.4 6 10.08(w), and 260.3 6 14.08(x),22 cor-responding to the most populated MD family. An average of 29crystal structures found angles of 67.0 6 10.58(/), 178.5 613.78(w), and 66.0 6 12.88(x),22 corresponding closely to thesecond most populated MD family. NMR spectroscopy on thislinkage found values of 70 6 208(/) and 2170 6 208(/) and60.6 6 208(x), also corresponding to the second most populatedMD family.35 The oligosaccharide MD simulation significantly

Tab

le1.

(Con

tinu

ed)

Disaccharides

12-M

era

Exp

erim

ental

Linkage

Phi

Psi

Omega

%Phi

Psi

Omega

%Phi

Psi

Omega

#

a-D-M

an-(1?

6)-b-D-M

an

(a,"

sc,ap,gg)

78.5

177.8

271

.367

81.2

169.5

269

.35

64.7

610

.4217

8.46

10.0

260

.36

14.0

38X-ray

22

(a,"

sc,ap,gt)

75.0

217

3.4

72.2

1565

.416

7.6

69.7

\1

67.0

610

.517

8.56

13.7

66.0

612

.829

X-ray

22

706

20217

06

2060

.66

20NMR35

(a,"

sc,"

sc,gg)

80.7

95.3

273

.314

81.4

94.4

267

.091

(a,"

sc,ap,tg)

77.4

217

8.1

159.0

3

(a,"

sc,"

sc,gt)

61.0

53.3

53.3

259

.46

7.5

94.0

617

.568

.56

12.3

29X-ray

22

(a,"

sc,"

sc,gt)

74.8

95.3

86.6

\1

(a,"

sc,2

sc,gt)

96.3

276

.589

.41

99.2

269

.497

.71

2?3

a-D-N

euAc-(2?3)-b-D-G

al(a,2

sc,ap)

236

.7214

2.5

93236

.0/2

36.3

214

0.5/214

3.1

90/92

243

.56

14.8

213

9.36

17.8

8NMR37–40,42–44

(averaged)

(a,"

sc,ap)

39.5

214

0.5

745

.7/42.6

214

3.2/214

5.8

10/8

68.5

613

.6212

5.1"

15.5

14X-ray

22

Populationpercentagesaregivenforeach

conformation.

Whentwovalues

arepresent,thefirstvaluecomes

from

the1?

6branch,whereas

thesecond

valuecomefrom

the1?

3branch.

*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.yThis particular disaccharide underwent a ring flip during the simulation.The system was resimulated with igb ! 5, resulting in a stable 4C1 ring.

Thus, for the remainder of the article the results computed with igb ! 5

will be used.



populates two of these families, with 91% clustered around818(/), 948(w), and 2678(x), and 5% clustered around 818(/),1708(w), and 2698(x). The remaining two families are popu-lated by less than 5%. Interestingly, one of these families is notseen in the disaccharides but is seen experimentally, with anaverage angle (29 crystal structures) of 59.4 6 7.58(/), 94.0 617.58(w), and 68.5 6 12.38(x).22

The a-D-Man-(1?3)-b-D-Man-OMe disaccharide populates asingle family clustered around 798(/) and 21078(w) for theentire simulation. This corresponds well with the experimentalaverage values of 71.5 6 8.88(/) and 2120.6 6 16.88(w)obtained from 130 crystal structures,22 as well as NMR valuesof 75 6 158(/) and 2135 6 158(w), 808(/) and 21308(w),1008(/) and 2908(w), and 80 6 15(/) and 2116 625(w).35,7,19 Nearly the same conformation is populated in theoligosaccharide simulation, with 94% clustered around 798(/)and 21208(w), and a new family that is clustered around1568(/) and 2718(w) with 6% population.

The b-D-GlcNAc-(1?2)-a-D-Man-OMe disaccharide popu-lates four families during the MD simulation, with 94% clus-tered around 2748(/) and 2838(w), and the remaining threefamilies having less than 5% occupancy. The major family cor-responds well to the experimentally averaged values of 280.1 612.68(/) and 297.6 6 22.38(w), obtained from 53 crystal struc-tures.22 NMR experiments have determined /- and w-values of2808(/) and 2908(w), and 292 6 168(/) and 283 6148(w),35 both corresponding to the most populated MD family.A second experimental family is seen, with average angles of58.3 6 9.48(/) and 287.2 6 15.28(w) as determined over eightcrystal structures.22 This family is observed in the disaccharidesimulation with a population of 1%, whose angles have an aver-age value of 548(/) and 2908(w). The b-D-GlcNAc-(1 ? 2)-a-D-Man linkage is present twice in the oligosaccharide, each clus-tered 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 populatesthree families during the MD simulation, with 69% clusteredaround 2698(/) and 1248(w), 30% clustered around 21218 (/)and 908(w), and less than 1% clustered around 538(/) and1228(w). An average of 28 crystal structures found average anglesof 271.4 6 10.98(/) and 132.2 6 7.48(w),22 corresponding to themost populated MD family. In agreement with these findings arefive NMR whose //w values include 296 6 5/154 6 3, 275 64/138 6 4, 287 6 10/146 6 11, 274/138, and 275/139.21,36

The two most populated families are also observed in bothbranches of the oligosaccharide. The 1?6 branch possesses 43%of the population clustered around 2758(/) and 1228(w), whereasthe 1?3 branch possesses 84% of the population clustered around2718(/) and 1258(w). For the second family the 1?6 branch pos-sesses 44% of the population clustered around 21118(/) and908(w), whereas the 1?3 branch possesses 12% of the populationclustered around 21378(/) and 888(w). A third family is popu-lated in the oligosaccharide, one that is not seen in the disaccha-rides, with a population of 11% clustered around 2878(/) and2658(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 disaccharidepopulates two families during the MD simulation, with 93% clus-

tered around 2378(/) and 21428(w), whereas the remaining fam-ily is clustered around 408(/) and 21408(w). In terms of a-D-NeuAc-(2?n) linkages, the 2?3 linkage has the most availableNMR6,21,37–43 and X-ray experimental data.22 The NMR studiesare coupled with computations to provide values for the /- andw-angles that are consistent with the NMR spectra. Eight NMRvalues yielded a /- and w-values of 243.58 6 14.88 and 2139.386 17.88,37–40,42–44 corresponding to the most populated MD con-formation. One NMR study yielded a values of 358 and 21088,43

whose /-value corresponds to the less populated MD family. Anaverage 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 bythe disaccharide MD simulation at 7%. The oligosaccharide simu-lation 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(/) and21448(w) in the 1?6 and 1?3 branches, respectively.

Discussion

Conformational Space of Carb-Rama Plots for IdealLinkage Angles

Recently, da Silva and coworkers presented a nice discussion ofthe anomeric and exo-anomeric effect in carbohydrates.45 Theanomeric effect refers to the thermodynamic preference for theaxial (a) position of electronegative groups (e.g., methoxy orcarbohydrate) over the beta (b) position at the anomeric C1

atom. Quantifying this is the angle C50##O5

0##C10##Ox (h),

where a has a h-angle of 608 and b has a y-angle of 1808.{ Theexo-anomeric effect refers to the preference for conformationsabout the /-angle. The /-angle may adopt conformations cen-tered around 2608 (2sc, synclinal or gauche), 608 ("sc), and1808 (ap, antiperiplaner or trans).45,46 Considering only the h-and /-angles for two-bond glycosidic linkages (e.g., 1?2, 1?3,2?3. . .), the relative order in increasing stability, based on QMcalculations on 2-methoxytetrahydropyran, is (a, "sc), (b, 2sc),(a, ap), (b, "sc), (b, ap), and (a, 2sc).45,46 Including the w-angle results in 18 possible conformations defined by (a, /, w)and (b, /, w).§ Including the x-angle for the 1?6 glycosidiclinkage results in 54 possible conformations defined by (a, /, w,x) and (b, /, w, x), whose ideal angles are presented in Table2. The common nomenclature for the x-angle is gauche–trans(gt), trans–gauche (tg), and gauche–gauche (gg), referring to thex-angle and O6##C6##C5##C4, respectively. The gt, tg, and ggconformations have x-angle values of approximately 608, 1808,and 2608, respectively. As a nomenclature example, (a, "sc,2sc, gt) indicates a conformation about an a 1?6 linkage thatpossesses a positive gauche /-angle, a negative gauche w-angleand a gt x-angle. Based on these ideal angles, the carb-Ramaplot for any two-bond a-linkages, will have nine regions of

{The exception to this is a-D-NeuAc-, where the a conformation pos-

sesses 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.



possible conformational space, with each region enclosed by a1208 3 1208 (w 3 /) area as shown in Supplementary Figure 1.The same will be true for the carb-Rama plots for any two-bondb-linkages. The three-dimensional carb-Rama plots for anythree-bond a- or b-linkage (e.g., 1?6, 2?6) will have 27regions of possible conformational space, each enclosed by a1208 3 1208 3 1208 (w 3 / 3 x) volume. However, not all ofthe conformational regions may be accessible due to energeticrestraints, while other regions may be preferentially populated.

Finally, in the situations where angles adopt a value that bor-ders two regions, we will indicate this by a ‘‘|’’ in the conforma-tion nomenclature. For example if an MD simulation samplesconformations that possess /-angles in the "sc and ap regions,but all of the conformations belong to a single / family, thefamily would be indicated by (b, "sc, "sc|ap). The angles thatfall into this category have angle values that are 1208 6 58 or21208 6 58.

Linkage Conformations from Simulations and Experiment

The carb-Rama plots for b-D-GlcNAc-(1?2)-a-D-Man show thatthe major family populated by the disaccharide and the oligosac-

charide is (b, 2sc, 2sc). In the oligosaccharide this linkagebehaves similarly in the 1?3 and 1?6 branches. The 1?6branch linkage has the average /-angle shifted by approximately2178, whereas the w-angle resembles that of the disaccharideand the 1?3 branch. This shift can be explained by the 1?6linkage forming multiple contacts with the inner carbohydrates,exemplified in Figure 5a, which induces the shift in its averageangle adopted. The disaccharide also has a (b, 2sc|ap, ap) con-formation that is populated for 4% of the simulation time. Theremaining two conformational families are (b, "sc, 2sc) and (b,2sc, "sc), both having very low populations (i.e., $1%).

The carb-Rama plots for the b-D-GlcNAc-(1?4)-b-D-GlcNAclinkage are very similar for both the disaccharide and the oligo-saccharide, adopting essentially 100% of the (b, 2sc, "sc|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, "sc) conformational space, while retaining (b, 2sc,"sc|ap) as the most abundant family in the disaccharide and oli-gosaccharide simulations. Interestingly, the carb-Rama plots forthe b-D-Man-(1?4)-b-D-GlcNAc linkage shows a 21% popula-tion shift between the disaccharide and oligosaccharide simula-tions. The most abundant family is populated 80% of the time in

Table 2. Nomenclaturea and ideal torsion angles for the 18 and 54 possible conformations for two-and

three-bond glycosidic linkages, respectively.

y / w x y / w x y / w x

Two-bond glycosidic linkage (e.g. 1?2,1?3, 1?4)

(a,"sc,"sc) 60 60 60 (a,ap,"sc) 60 180 60 (b,2sc,"sc) 180 260 60

(a,"sc,2sc) 60 60 260 (a,ap,2sc) 60 180 260 (b,2sc,2sc) 180 260 260(a,"sc, ap) 60 60 180 (a,ap,ap) 60 180 180 (b,2sc,ap) 180 260 180

(a,2sc,"sc) 60 260 60 (b,"sc,"sc) 180 60 60 (b,ap,"sc) 180 180 60

(a,2sc,2sc) 60 260 260 (b,"sc,2sc) 180 60 260 (b,ap,2sc) 180 180 260(a,2sc,ap) 60 260 180 (b,"sc,ap) 180 60 180 (b,ap,ap) 180 180 180

Three-bond glycosidic linkage (e.g. 1?6)

(a,"sc,"sc,gt) 60 60 60 60 (a,ap,"sc,gt) 60 180 60 60 (b,2sc,"sc,gt) 180 260 60 60

(a,"sc,"sc,gg) 60 60 60 260 (a,ap,"sc,gg) 60 180 60 260 (b,2sc,"sc,gg) 180 260 60 260(a,"sc,"sc,tg) 60 60 60 180 (a,ap,"sc,tg) 60 180 60 180 (b,2sc,"sc,tg) 180 260 60 180

(a,"sc,2sc,gt) 60 60 260 60 (a,ap,2sc,gt) 60 180 260 60 (b,2sc,2sc,gt) 180 260 260 60

(a,"sc,2sc,gg) 60 60 260 260 (a,ap,2sc,gg) 60 180 260 260 (b,2sc,2sc,gg) 180 260 260 260(a,"sc,2sc,tg) 60 60 260 180 (a,ap,2sc,tg) 60 180 260 180 (b,2sc,2sc,tg) 180 260 260 180

(a,"sc, ap,gt) 60 60 180 60 (a,ap,ap,gt) 60 180 180 60 (b,2sc,ap,gt) 180 260 180 60

(a,"sc,ap,gg) 60 60 180 260 (a,ap,ap,gg) 60 180 180 260 (b,2sc,ap,gg) 180 260 180 260

(a,"sc,ap,tg) 60 60 180 180 (a,ap,ap,tg) 60 180 180 180 (b,2sc,ap,tg) 180 260 180 180(a,2sc,"sc,gt) 60 260 60 60 (b,"sc"sc,gt) 180 60 60 60 (b,ap,"sc,gt) 180 180 60 60

(a,2sc,"sc,gg) 60 260 60 260 (b,"sc,"sc,gg) 180 60 60 260 (b,ap,"sc,gg) 180 180 60 260

(a,2sc,"sc,tg) 60 260 60 180 (b,"sc,"sc,tg) 180 60 60 180 (b,ap,"sc,tg) 180 180 60 180

(a,2sc,2sc,gt) 60 260 260 60 (b,"sc,2sc,gt) 180 60 260 60 (b,ap,2sc,gt) 180 180 260 60(a,2sc,2sc,gg) 60 260 260 260 (b,"sc,2sc,gg) 180 60 260 260 (b,ap,2sc,gg) 180 180 260 260

(a,2sc,sc,tg) 60 260 260 180 (b."sc,2sc,tg) 180 60 260 180 (b,ap,2sc,tg) 180 180 260 180

(a,2sc,ap,gt) 60 260 180 60 (b,"sc,ap,gt) 180 60 180 60 (b,ap,ap,gt) 180 180 180 60

(a,2sc,ap,gg) 60 260 180 260 (b,"sc,ap,gg) 180 60 180 260 (b, ap,ap,gg) 180 180 180 260(a,2sc,ap,tg) 60 260 180 180 (b,"sc,ap,tg) 180 60 180 180 (b,ap,ap,tg) 180 180 180 180

aTwo-bond glycosidic linkages are defined by (a, /, w) and (b, /, w), and three-bond glycosidic linkages are definedby (a, /,w,x) and (b, /,w,x). Torsion definitions: a/b ! C0

5##O05##C0

1##Ox; / ! O05##C0

1##Ox##Cx; w !C0##Ox##Cx##Cx-1; x ! O6## C6##C5##O5. The abbreviations 2sc,"sc and ap refer to an angle adopting a value

that is 2608 (negative synclinal or gauche), "608 (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 inthe x angle and O6##C6##C5##C4, respectively.



the disaccharide, which reduces to 59% in the oligosaccharide.Concurrently, the new and second most abundant family goesfrom a 20% population in the disaccharide to 41% population inthe oligosaccharide. The increase in the oligosaccharide’s (b,2sc|ap, "sc) family is due to the 1?6 branch interacting withthe inner core carbohydrates, such that the 1?6 branch liesbehind the fucose residue Figure 5b.

The other 1?4 linkage, b-D-Gal-(1?4)-b-D-GlcNAc, dis-plays similar traits to those mentioned above, with (b, 2sc,"sc|ap) being the most abundant family and (b, 2sc|ap, "sc)being the second most abundant family. As in the b-D-Man-(1?4)-b-D-GlcNAc linkage, there is a shift that occurs betweenthese families. The b-D-Gal-(1?4)-b-D-GlcNAc linkage presentin the oligosaccharide’s 1?6 branch accesses a new conforma-tion, (b, 2sc, 2sc), for 11% of the simulation time, which is inaddition to the equally populated (b, 2sc, "sc|ap) and (b,2sc|ap, "sc) families at %44%. This is not the case in the 1?3branch, where the (b, 2sc,"sc|ap) family increases in populationby 15% relative to the disaccharide. The populated (b, 2sc|ap,"sc) and (b, 2sc, 2sc) families have significantly reduced oc-cupancy of 12% and 3%, respectively.

The a-D-Man-(1?3)-b-D-Man linkage has the (a, "sc, 2sc)family populated for 100% of the disaccharide simulation, and94% of the oligosaccharide simulation. The oligosaccharide pos-sesses an additional conformation, (a, ap, 2sc), with a 6% popu-lation. This new conformation occurs when the 1?3 branchwraps back to interact with the inner core carbohydrates, form-ing a stacked topology as exemplified in Figure 5c.

The carb-Rama plots for a-D-NeuAc-(2?3)-b-D-Gal indicatethat the (a, 2sc, ap) conformation is the most dominate familyin both simulations, with 93% population in the disaccharide,and 90% and 92% in the 1?6 and 1?3 oligosaccharidebranches, respectively. This family is seen in nearly all NMRstudies. The less populated MD family is (a, "sc, ap), with10% or less occupancy, which is not seen experimentally. How-ever, the closely related family, (a, "sc, 2sc|ap), is seen inX-ray experiments. Of the residues studied here, a-D-NeuAc-proved the most challenging to parameterize due to its potentialto be ionized in solution and the number of mixed functional-ities that govern the /-angle torsion.1 These results suggest that arevisit of the a-D-NeuAc parameterization might be warranted.

In all simulations involving the 1?6 linkage, the x-anglepredominately 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’’ x-angle curve, which will be qualitatively similar to the repulsive

curve presented for a-D-glucopyranoside that we presented pre-

viously.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 inter-

actions. 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 hydro-

gen bond donor, which would marginally stabilize the tgconformation.

The carb-Rama plots for the a-L-Fuc-(1?6)-b-D-GlcNAclinkage are similar between the disaccharides and the oligosac-

charide, both primarily populating an (a, 2sc, "sc, gg) confor-mation. Five other families are populated, which include (a,2sc, ap, gt), (a, 2sc, 2sc, gt), (a, 2sc, "sc, gg), (a, 2sc, ap,

tg), and (a, 2sc, "sc, gt). This linkage adopts a single /-angleconformation 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. Inthis conformation, the /-angle distorts to avoid steric hinderence

between the ##NHC(!!O)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-angleadopting a conformation that allows for more favorable contacts

with the 1?6 branch.

Figure 5. The representations of three oligosaccharide conformations that were sampled during theMD simulations, labeled A, B, and C. The blue residues are the carbohydrates belonging to the 1 ? 6branch, the red represent the carbohydrates on the 1 ? 3 branch, and the traditionally colored residuesare the inner core of the oligosaccharides.



The carb-Rama plots for a-D-Man-(1?6)-b-D-Man show asignificant shift in populations when comparing the disaccharideswith the oligosaccharide. The largest shift occurs with the (a,"sc, ap, gg) conformation, which is the dominant conformationin the disaccharide (67%) to the second most dominant confor-mation (5%) in the oligosaccharide. This corresponds to anincrease in the third most populated disaccharide conformation,(a, "sc, "sc, gg) (14%), which becomes the most dominantconformation (91%) in the oligosaccharide. Interestingly, the x-angle preferentially adopts a gg conformation that is long livedin the oligosaccharide, which is contrary to the frequent sam-pling observed in the disaccharide simulations. Thus, the addi-tion 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 MDsimulations correspond well with available experimental data.The most populated family in each linkage is experimentallyobserved in X-ray or NMR spectroscopy. By comparing the aver-age MD value (Table 1) with the average X-ray values deter-mined by Wormald and coworkers,22 the /-, w-, and x-angles aremodeled very well, with an average absolute difference from theX-ray of 10.38, 12.68, and 14.08, respectively. The largest /-angledifference occurs in the oligosaccharide for b-D-Man-(1?4)-b-D-GlcNAc linkage’s (b, 2sc, "sc|ap) conformation and for a-D-Man-(1?6)-b-D-Man linkage’s (b, "sc, ap, gg) conformation,with an absolute difference of 16.58 and 16.38, respectively.

The largest w-angle difference, with respect to the average crys-tal values, occurs in the disaccharide and oligosaccharide a-L-Fuc-(1?6)-b-D-GlcNAc linkage (a, 2sc, ap, gg) conformation, withabsolute values of 32.98 and 35.98, respectively. The third largestw-angle difference occurs at an absolute value of 14.68 in the disac-charide b-D-GlcNAc-(1?2)-a-D-Man’s linkage. Additionally, thea-D-NeuAc-(2?3)-b-D-Gal’s (a, 2sc, ap), when compared with theaverage NMR values, has an absolute differences of less than 78.

The largest x-angle difference, with respect to the averagecrystal values, occurs in the disaccharide and oligosaccharidea-L-Fuc-(1?6)-b-D-GlcNAc linkage’s (a, 2sc, ap, gg) confor-mation, with absolute values of 13.48 and 23.48, respectively.Likewise, the average MD values compare very well with avail-able NMR data,7,19,21,35,36 with an average absolute differencefor /- and w-angles of 8.68 and 15.28, respectively. Only oneNMR determined x-angle is known, a-D-Man-(1?6)-b-D-Man’s(b,"sc,ap,gg) linkage, and the disaccharide and oligosaccharidesimulations are within 11.48 and 9.48, respectively.

General Trends

b-D-(1?4)-equatorial: In this study, there are three different car-bohydrate combinations that belong to this linkage type: b-D-GlcNAc-(1?4)-b-D-GlcNAc, b-D-Man-(1?4)-b-D-GlcNAc, andb-D-Gal-(1?4)-b-D-GlcNAc. The two significant conformationsthat these b-(1?4)-equatorial linkages occupy in the simulationsare (b,2sc,"sc|ap) and (b,2sc|ap,"sc). The average of 376crystal structures that possess a b-D-GlcNAc-(1?4)-D-GlcNAclinkage yields average /- and w-angles of 275.98 6 11.68 and119.086 15.48,22 respectively, placing them in the (b,2sc,"sc|ap)

region. The average of 28 crystal structures that possess a b-D-Gal-(1?4)-D-GlcNAc linkage yields average /- and w-angles of2718 6 108 and 132.28 6 7.48,22 respectively, placing them inthe (b,2sc,ap) region. The average of 197 crystal structures thatpossess 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 respec-tively, placing them in the (b,2sc,"sc) region. NMR spectros-copy on Lactose (b-D-Gal-(1?4)-b-D-Glc) and Cellobiose (b-D-Glc-(1?4)-b-D-Glc) yields a /-angle of approximately 2878 anda w-angle of approximately 998, placing these two linkages in the(b,2sc,"sc) region.50,51 The average of two crystal structures thatpossess 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 respec-tively, placing them in the (b,ap,sc) region. This data taken to-gether suggest that b-D-(1?4)-equatorial linkages preferentiallydominate the (b,2sc,"sc|ap) region, whereas the (b, sc|ap,"sc),(b,2sc,ap), (b,2sc,2sc), and (b,ap,"sc) regions are accessible toa lesser degree.

a-D-(1?3)-equatorial: The a-D-Man-(1?3)-b-D-Man linkagepreferentially populates the (a,"sc,2sc) region of the carb-Ramaplot. There are 130 crystal structures that possess an a-D-Man-(1?3)-D-Man linkage whose average /- and w-angles are 71.58 68.88 and 2120.68 6 16.88,22 respectively, placing an average crystalstructure at (a,"sc,2sc|ap). In addition to this specific linkage, thereis NMR data available for Nigerose (a-D-Gal-(1?3)-b-D-Glc),whose conformation is in the (a,"sc,ap) region with a /-angle of818 and a w-angle of 21438.50 These values suggest a strong a-D-(1?3)-equatorial linkage preference for the (a,"sc,2sc) and(a,"sc,ap) regions.

a-D-(1?6)-equatorial: This linkage is the most difficult typefor which to provide general trends. The a-D-Man-(1?6)-b-D-Man linkage populates three significant areas in the carb-Ramaplots, which are (a,"sc,ap,gg), (a,"sc,ap,gt), and (a,"sc,"sc,gg).There are 96 crystal structures that possess an a-D-Man-(1?6)-D-Man linkage occupying the regions (a,"sc,ap,gg), (a,"sc,ap,gt)and (a,"sc,"sc,gt) whose average /-, w-, and x-angles in regionone are 64.78 6 10.48, 2178.48 6 10.08, and 260.38 6 14.08, inregion 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 68.58 612.38,22 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,"sc,ap,gg), (a,"sc,ap,gt), (a,"sc,"sc,gg), and (a,"sc,"sc,g").

The MD simulations show that the a-L-Fuc-(1?6)-b-D-GlcNAc linkage significantly populates the (a,2sc,ap,gg) and(a,2sc,ap,gt) regions. Fucose posses an L configuration, whichcauses the preferred /-angle conformation of "608, as found inthe other a-D-(1?6)-equatorial linkages, to become 2608 forthis linkage. The three dimensional geometry of these regions issimilar for both the a-D-(1?6)-equatorial and a-L-(1?6)-equato-rial, with a gauche conformation in the /-angle and a trans con-formation in the C20##C10##O6##C6 torsion angle.

Conclusion

In this article, we present the extension of G.N. Ramachandran’sidea of plotting the amino acid phi and psi angles to the glyco-



sidic phi, psi and omega angles formed between carbohydrates.Considering two-bond glycosidic linkages, there are 18 possibleconformational regions that can be defined by (a, /, w) and (b,/, w), whereas for three-bond linkages there are 54 possibleregions that can be defined by (a, /, w, x) and (b, /, w, x).We have reported the results of an implicitly hydrated moleculardynamics simulation on an oligosaccharide composed of 12carbohydrate residues, and on the eight constituent disaccharidesthat compose this oligosaccharide.

The Glycam06 force field reproduces known experimentaldata well, where the average /-, w-, and x-angles of major MDconformational families correspond well with available experi-mental data. The most populated family for each linkage isexperimentally observed in X-ray or NMR spectroscopy. Bycomparing the average MD values to the average X-ray valuesdetermined by Wormald and coworkers,22 the /-, w- and x-angles are modeled very well, with an average absolute differ-ence from the X-ray values of 10.38, 12.68, and 14.08, respec-tively.

Three general trends can be seen in the carb-Rama plots andexperimental data. First, the b-(1?4)-equatorial linkages pre-ferentially dominate the (b,2sc,"sc|ap) region, whereas the(b,2sc|ap,"sc), (b,2sc,ap), (b,2sc,2sc), and (b,ap,"sc) regionsare accessible to a lesser degree. Second, a-(1?3)-equatoriallinkages show a strong preference for the (a,"sc,2sc) and(a,"sc,ap) regions. Third, the a-D-(1?6)-equatorial linkagespreferentially populate the regions (a,"sc,ap,gg), (a,"sc,ap,gt),and (a,"sc,"sc,gg).

The reported simulation results and the carb-Rama plots willbe useful for future oligosaccharide studies in determining thefactors that cause specific glycosidic linkage conformations tobe adopted. We hope that this presentation of carb-Rama plotswill aid others in unraveling the complex structure of di-, poly-,and oligosaccharides.

Acknowledgments

Acknowledgment is made to NSF, NIH and to Hamilton Collegefor support of this work. This project was supported in part byNIH grant, NSF grant, and by NSF Grants as part of theMERCURY highperformance computer consortium (http://mercury.chem.hamilton.edu).

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Ramachandran-type plots for glycosidic linkages: Examples...

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