Directory UMM :wiley:Public:journals:jcc:suppmat:17:

Supplement To:
Parametrization of the GROMOS Force Field for
Oligosaccharides and Assessment of the Efficiency of
Molecular Dynamics Simulations

Karl-Heinz Ott1 and Bernd Meyer2

Complex Carbohydrate Research Center and Departments of Biochemistry
and Chemistry, The University of Georgia, 220 Riverbend Rd., Athens, GA
30602, USA

Present Addresses:
1) American Cyanamid Co., P.O. Box 400, Princeton, NJ 08543-0400, USA and
2)

Institut

Germany

für

Organische

Chemie,

M.L.

King

Platz

6,

20146

Hamburg,

Cluster analysis:
A complete, hierarchical clustering algorithm1,2 was used to group the
conformations that were represented by sine and cosine values of selected
dihedral angles.

defined by the

ϕ

For run w60, a four dimensional conformational space was
and

ψ

angles and by two intra-ring dihedral angles (O5-C1-

C2-C3) that are characteristic for the ring conformations. The statistical data
analysis

package

BLSS3

was

used

to

generate

conformations observed in 300 fs intervals.

the

cluster

tree

for

The resulting cluster tree was

analyzed statistically and an appropriate cutting level was chosen.
remaining conformations, sampled in 100 fs steps, were

nearest cluster.

the

sorted

The

into

the

Conformations that differed by more than 1.5 times the

standard deviations from the cluster definitions were rejected.
procedure but with the

ϕ, ψ ,

and the both

ω

The same

angles as parameters for the

clustering was used to classify the results of the other MD simulations of this
work (data only shown for run w).
1

J.A. Hartigan, Clustering

Algorithms,Wiley, New York, 1975.

2

B.Everitt, Cluster

3

D.M. Abraham and F. Rizzardy, The Berkley Interactive Statistical

Analysis
, Halsted, New York, 1980.

System, Norton, NY 1988.

Run w
The

data

set

was

split

into

6

clusters,

each

having

a

correlation

coefficient of its associated conformations of between 0.3 and 0.7 (Tab. SII).
The

highest

populated

cluster

with

a

population

of

32%

has

a

gg

conformation in the reducing ring and a gt conformation in the nonreducing
ring with the glycosidic linkage at

cluster

with

22%

population

hydroxymethyl groups but has

ϕ

≈

has
and

ψ

-40o/-40o.

the
at

≈

same
0o.

Another highly populated
conformations

of

the

The same glycosidic linkage

conformation with both hydroxymethyl groups in a gg conformation is found
in another cluster with 11% population.
cluster that has average

ϕ

and

ψ

angles of

24% of the conformations form a

≈

-30o which are the angles found

in X-ray crystal studies (F. Takusagawa and G.A. Jacobson, Acta Cryst,
Cryst, B34,
213. 1978). In this cluster the

ω

angles are oriented in the gg and the tg

position for the reducing and the nonreducing residue, respectively (cf. Tab.
SII).

A cluster with 7.5% of the total population has both

2

ω

dihedral angles in

a

gt

ϕ /ψ

conformation.

The glycosidic linkage of this cluster is characterized by

values of ≈ -10o.

As is evident from the populations of the hydroxymethyl groups, the MD
simulation was not run for a long enough time to give correct statistics of the
populations of different minima, which is even true for the most populated
minima.

Run w60
The cluster analysis resulted in 19 clusters (Tab. SIII).

Based on the

analysis of the transition rates between the clusters four major groups of
clusters can be identified (cf. Tab. SIII).

They are characterized by the

differences in the conformations of the glucose rings and have the glycosidic
linkage in conformations close to the global minimum.

4C
1

conformers have both hexose rings in the

Only 18% of the

orientation.

In 64% of the

simulation either the reducing or the nonreducing ring has the inverted
ring conformation.

In 17% of the simulation both rings adopted the

1C
4
1C
4

conformation.
The cluster analysis revealed that the accessible range of the glycosidic

4C
1

linkage space is significantly dependent on the ring conformations.

conformers restrict the conformational flexibility of the glycosidic linkage
compared

to

the

1C
4

conformers.

The

strongest

effect

1C -1C
4
4

comparing the conformational space accessible to the
that of the 4C1-4C1 species
minimum of the 4C1-4C1
previously

described

is

found

when

species with

(Fig. 1a,d).

The position and size of the global

conformers

is

calculations

at

similar

350K

and

to

those

400K.

found
The

in

the

additional

conformational flexibility apparent from the conformational space totally
accesses at 600K (Fig. 1, hatched area) originates from a glucose in an
inverted

1C
4
1b).

1C
4

conformation (Fig. 1b-d).

conformation, the

ϕ/ψ

When the nonreducing residue is in a

contour extends to more negative

In contrary, when the reducing residue adopts a

the nonreducing residue has the

4C
1

conformation the

1C
4

ϕ/ψ

ϕ

angles (Fig.

conformation and

contours extend to

more positive values (Fig. 1c). In the fourth group of clusters, with both rings
in the

1C
4

conformation, the

ϕ/ψ

contour shows the increased flexibility to

more negative ψ angles as well as to more positive
ϕ and
Two

small

clusters

glycosidic linkage.

show

up

for

the

inverted

ψ

angles (Fig. 1d).

conformation

of

the

This inverted conformer remains stable for about 4 ps
3

while the hexose ring conformations are both in
with

ψ

4C .
1

Some of the conformers

around 180o are found during the time of conformational transitions

of the nonreducing glucose residue.

4

Table S I:
Energy averages of the MD simulations.

The total energies (Tot) together

with their standard deviations (Std) and the change in the total energy over
the entire run (Slp) calculated from a linear regression analysis are given for
the MD simulations, wb1, wb2, w, w35, w40, w60 and the in vacuo MD
simulations.

Additionally, the total kinetic energy (Kin) the total potential

Energy (Pot), the electrostatic energy terms for the maltose (El-malt), for the
water (El-wat) and for the maltose-water interaction (El-mw) as well as the
corresponding van-der
van-der-Waals
-Waals energy terms (LJ-malt, LJ-wat, and LJ-mw) are
listed. The sum of the bond angle and dihedral energies are in column (Bond).
The average energy terms for the six MD simulations in water (AVG water),
and for the three in vacuo MD simulations (AVG vacuo) are also displayed.
ND: not determined.

Run

Tot

Std

Slp

Kin

Pot

Bond

EL-malt

LJ-malt

El-mw

LJ-mw

El-wat

LJ-wat

wb1 200ps

-14342

177

0

4279

-18621

127

573

-24

-420

-96

-21889

3109

wb2 500ps

-14443

178

-129

4273

-18717

46

572

-21

-424

-97

-21904

3111

w 250ps

-3741

74

nd

1201

-4942

123

492

-21

-401

-90

-5909

865

w35 200ps

-3220

69

14

1353

-4573

137

574

-20

-397

-88

-5556

777

w40 200ps

-2704

64

13

1559

-4263

148

573

-20

-371

-90

-5218

715

w60 950ps

-1055

64

5

2301

-3356

189

572

-18

-305

-93

-4303

601

589

6

1

68

522

120

420

-18

va 500ps
vb 500ps

591

6

1

68

523

126

414

-16

vc 500ps

670

4

1

68

602

139

480

-18

Avg water
Avg wb
Avg vacuo

-6584

2494

-9078

128

559

-21

-386

-92

-10797

1529

-14393

4276

-18669

86

572

-22

-422

-96

-21896

3110

617

68

549

128

438

-17

5

Table SII:
Statistic of the cluster analysis of run w that used sine and cosine values of
the

ϕ, ψ

ω

and both

dihedral angles as parameters for the cluster definition.

The population (Pop) of the six clusters together with their average

ϕ

and

ψ

angles, their hydroxymethyl group orientation of the reducing (ω1) and the
nonreducing (ω2) glucose are listed.

The last column contains the correlation

coefficient (Cor) that are calculated from correlating the vectors defined by
the four dihedral anglesϕ,

Pop % P
806
32

ϕ

-45

ψ

-39

ψ

ω 1−ω 2
gg-gt

and

ω1,2.

Cor
0.47

597

24

-22

-26

gg-tg

0.35

564

23

-1

-2

gg-gt

0.42

283

11

0

-1

gg-gg

0.65

184

7

-13

-10

gt-gt

0.33

66

3

-29

-31

tg-gt

0.44

6

Table SIII:
Cluster statistics from a cluster analysis of MD simulation w60.
(Avg) and standard deviation (Std) of the

ϕ

and

ψ

dihedral angles and the

average total energy (E-tot) are tabulated for all 19 clusters.
sorted

by

the

conformation

of

the

glucose

rings.

The average

The clusters are

Clusters

representing

inverted glycosidic linkage conformations are listed separately at the bottom
of the table.

For each group, the total population and the group averages and

standard deviations are added in bold font (Sum).

Red NR

Glucose

Popu-

Pop ϕ
ψ
% Avg Std Avg Std kJ/mol

E-tot

lation

4C1 4C1

274

4C1 4C1

139

16

-66

8

-40

10

-1061

8

-56

9

-61

7

-1070

4C1 4C1

75

4

-39

14

-83

14

-1039

4C1 4C1

625

36

-30

19

-11

15

-1065

4C1 4C1

415

24

-28

15

-43

11

-1050

4C1 4C1

110

6

-52

15

-25

20

-1032

4C1 4C1

61

4

-87

16

-35

15

-1046

1738

18

-41

15

-28

13

-1052

4C1 1C4

1244

50

-94

22

-25

20

-1050

4C1 1C4

1263

50

-48

17

-32

23

-1059

2507

26

-71

20

-29

22

-1055

1C4 4C1

1108

30

-23

26

26

29

-1049

1C4 4C1

254

7

-82

17

-37

20

-1058

1C4 4C1

1666

46

-48

11

-44

18

-1063

1C4 4C1

547

15

-18

12

-47

16

-1050

Sum

Sum

3655

38

-38

17

-18

22

-1055

1C4 1C4

Sum

222

14

-36

35

22

26

-1043

1C4 1C4

258

16

-137

21

-10

31

-1039

1C4 1C4

870

54

-76

15

-34

23

-1053

1C4 1C4

250

16

-35

20

-56

21

-1067

1600

17

-16

21

-26

25

-1051

4C1 4C1

39

33

-25

14

192

18

-1068

1C4 4C1

80

67

-32

18

169

38

-1032

119

1

60

17

181

33

-1050

Sum

Sum

7

Conformational Analysis of Oligosaccharides

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ϕ
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Figure 1:

The conformational space of the glycosidic linkage dihedral
angles

ϕ

displayed

and
in

ψ
all

occupied during MD simulation w60 at 600K
four

parts

of

the

figures

as

hatched

area.

Overplotted in a thick closed line, the conformational space is
indicated

4C -1C
1
4

for
C)

those

1C -4C
4
1

conformers
D)1C4-1C4

that

have

A)

4C -4C
1
1

B)

conformations of the reducing

and the nonreducing glucose's, respectively.

Lowest contours

and area boundaries are drawn at 10 percent of the height of
the highest populated bin.

8