ott_supl.doc 35KB Jun 05 2011 09:30:44 PM
Supplement To:
Parametrization of the GROMOS Force Field for
Oligosaccharides and Assessment of the Efficiency of
Molecular Dynamics Simulations
KarlHeinz 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 085430400, USA and
2) Institut für Organische Chemie, M.L. King Platz 6, 20146 Hamburg, Germany
Cluster analysis:
A complete, hierarchical clustering algorithm 1,2 was used to group the
conformations that were represented by sine and cosine values of selected dihedral
angles. For run w60, a four dimensional conformational space was defined by the
and angles and by two intraring dihedral angles (O5C1C2C3) that are
characteristic for the ring conformations. The statistical data analysis package
BLSS3 was used to generate the cluster tree for the conformations observed in 300
fs intervals. The resulting cluster tree was analyzed statistically and an
appropriate cutting level was chosen. The remaining conformations, sampled in
100 fs steps, were sorted into the nearest cluster. Conformations that differed by
more than 1.5 times the standard deviations from the cluster definitions were
rejected. The same procedure but with the , , and the both 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 Analysis, Halsted, New York, 1980.
3
D.M. Abraham and F. Rizzardy, The Berkley Interactive Statistical 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 40o/40o.
Another highly populated cluster with 22% population has the same conformations
of the hydroxymethyl groups but has and at 0o. The same glycosidic linkage
conformation with both hydroxymethyl groups in a gg conformation is found in
another cluster with 11% population. 24% of the conformations form a cluster that
has average and angles of 30o which are the angles found in Xray crystal
studies (F. Takusagawa and G.A. Jacobson, Acta Cryst, B34, 213. 1978). In this
cluster the 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 dihedral angles in a gt 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
2
close to the global minimum. Only 18% of the conformers have both hexose rings
in the 4C1 orientation. In 64% of the simulation either the reducing or the
nonreducing ring has the inverted 1C4 ring conformation. In 17% of the simulation
both rings adopted the 1C4 conformation.
The cluster analysis revealed that the accessible range of the glycosidic linkage
space is significantly dependent on the ring conformations. 4C1 conformers restrict
the conformational flexibility of the glycosidic linkage compared to the 1C4
conformers. The strongest effect is found when comparing the conformational
space accessible to the 1C41C4 species with that of the 4C14C1 species (Fig. 1a,d).
The position and size of the global minimum of the 4C14C1 conformers is similar to
those found in the previously described calculations at 350K and 400K. The
additional conformational flexibility apparent from the conformational space totally
accesses at 600K (Fig. 1, hatched area) originates from a glucose in an inverted 1C4
conformation (Fig. 1bd). When the nonreducing residue is in a 1C4 conformation,
the contour extends to more negative angles (Fig. 1b). In contrary, when the
reducing residue adopts a 1C4 conformation and the nonreducing residue has the
4C
1 conformation the contours extend to more positive values (Fig. 1c). In the
fourth group of clusters, with both rings in the 1C4 conformation, the contour
shows the increased flexibility to more negative angles as well as to more positive
and angles (Fig. 1d).
Two small clusters show up for the inverted conformation of the glycosidic
linkage. This inverted conformer remains stable for about 4 ps while the hexose
ring conformations are both in 4C1. Some of the conformers with around 180o
are found during the time of conformational transitions of the nonreducing glucose
residue.
3
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 (Elmalt), for the water (Elwat) and for the maltosewater
interaction (Elmw) as well as the corresponding vanderWaals energy terms (LJ
malt, LJwat, and LJmw) 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
wb1 200ps
wb2 500ps
w 250ps
w35 200ps
w40 200ps
w60 950ps
va 500ps
vb 500ps
vc 500ps
Avg water
Avg wb
Avg vacuo
Tot
Std Slp
-14342 177
0
-14443 178 -129
-3741
74 nd
-3220
69
14
-2704
64
13
-1055
64
5
589
6
1
591
6
1
670
4
1
-6584
-14393
617
Kin
4279
4273
1201
1353
1559
2301
68
68
68
2494
4276
68
Pot
Bond EL-malt LJ -malt El-mw LJ -mw El-wat LJ -wat
-18621 127
573
-24
-420
-96 -21889 3109
-18717
46
572
-21
-424
-97 -21904 3111
-4942 123
492
-21
-401
-90
-5909
865
-4573 137
574
-20
-397
-88
-5556
777
-4263 148
573
-20
-371
-90
-5218
715
-3356 189
572
-18
-305
-93
-4303
601
522 120
420
-18
523 126
414
-16
602 139
480
-18
-9078 128
559
-21
-386
-92 -10797 1529
-18669
86
572
-22
-422
-96 -21896 3110
549 128
438
-17
4
Table SII:
Statistic of the cluster analysis of run w that used sine and cosine values of the ,
and both dihedral angles as parameters for the cluster definition. The
population (Pop) of the six clusters together with their average and angles, their
hydroxymethyl group orientation of the reducing (1) and the nonreducing (2)
glucose are listed. The last column contains the correlation coefficient (Cor) that
are calculated from correlating the vectors defined by the four dihedral angles ,
and 1,2.
Pop % P
806 32
597 24
564 23
283 11
184
7
66
3
-45
-22
-1
0
-13
-29
1 2
-39 gg-gt
-26 gg-tg
-2 gg-gt
-1 gg-gg
-10 gt-gt
-31 tg-gt
Cor
0.47
0.35
0.42
0.65
0.33
0.44
5
Table SIII:
Cluster statistics from a cluster analysis of MD simulation w60. The average (Avg)
and standard deviation (Std) of the and dihedral angles and the average total
energy (Etot) are tabulated for all 19 clusters. The clusters are sorted by the
conformation of the glucose rings. 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 Popu
E-tot
Pop
Glucose lation
%
Avg Std Avg Std kJ/mol
4C1 4C1
274 16
-66
8
-40 10
-1061
4C1 4C1
139
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
Sum
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
Sum
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
3655 38
-38 17 -18 22 -1055
1C4 1C4
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
Sum
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
Sum
119
1
60 17 181 33 -1050
6
Figure 1:
The conformational space of the glycosidic linkage dihedral angles
and occupied during MD simulation w60 at 600K displayed in all
four parts of the figures as hatched area. Overplotted in a thick
closed line, the conformational space is indicated for those
conformers that have A) 4C14C1 B) 4C11C4 C) 1C44C1 D)1C4
1C
4 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.
7
Parametrization of the GROMOS Force Field for
Oligosaccharides and Assessment of the Efficiency of
Molecular Dynamics Simulations
KarlHeinz 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 085430400, USA and
2) Institut für Organische Chemie, M.L. King Platz 6, 20146 Hamburg, Germany
Cluster analysis:
A complete, hierarchical clustering algorithm 1,2 was used to group the
conformations that were represented by sine and cosine values of selected dihedral
angles. For run w60, a four dimensional conformational space was defined by the
and angles and by two intraring dihedral angles (O5C1C2C3) that are
characteristic for the ring conformations. The statistical data analysis package
BLSS3 was used to generate the cluster tree for the conformations observed in 300
fs intervals. The resulting cluster tree was analyzed statistically and an
appropriate cutting level was chosen. The remaining conformations, sampled in
100 fs steps, were sorted into the nearest cluster. Conformations that differed by
more than 1.5 times the standard deviations from the cluster definitions were
rejected. The same procedure but with the , , and the both 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 Analysis, Halsted, New York, 1980.
3
D.M. Abraham and F. Rizzardy, The Berkley Interactive Statistical 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 40o/40o.
Another highly populated cluster with 22% population has the same conformations
of the hydroxymethyl groups but has and at 0o. The same glycosidic linkage
conformation with both hydroxymethyl groups in a gg conformation is found in
another cluster with 11% population. 24% of the conformations form a cluster that
has average and angles of 30o which are the angles found in Xray crystal
studies (F. Takusagawa and G.A. Jacobson, Acta Cryst, B34, 213. 1978). In this
cluster the 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 dihedral angles in a gt 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
2
close to the global minimum. Only 18% of the conformers have both hexose rings
in the 4C1 orientation. In 64% of the simulation either the reducing or the
nonreducing ring has the inverted 1C4 ring conformation. In 17% of the simulation
both rings adopted the 1C4 conformation.
The cluster analysis revealed that the accessible range of the glycosidic linkage
space is significantly dependent on the ring conformations. 4C1 conformers restrict
the conformational flexibility of the glycosidic linkage compared to the 1C4
conformers. The strongest effect is found when comparing the conformational
space accessible to the 1C41C4 species with that of the 4C14C1 species (Fig. 1a,d).
The position and size of the global minimum of the 4C14C1 conformers is similar to
those found in the previously described calculations at 350K and 400K. The
additional conformational flexibility apparent from the conformational space totally
accesses at 600K (Fig. 1, hatched area) originates from a glucose in an inverted 1C4
conformation (Fig. 1bd). When the nonreducing residue is in a 1C4 conformation,
the contour extends to more negative angles (Fig. 1b). In contrary, when the
reducing residue adopts a 1C4 conformation and the nonreducing residue has the
4C
1 conformation the contours extend to more positive values (Fig. 1c). In the
fourth group of clusters, with both rings in the 1C4 conformation, the contour
shows the increased flexibility to more negative angles as well as to more positive
and angles (Fig. 1d).
Two small clusters show up for the inverted conformation of the glycosidic
linkage. This inverted conformer remains stable for about 4 ps while the hexose
ring conformations are both in 4C1. Some of the conformers with around 180o
are found during the time of conformational transitions of the nonreducing glucose
residue.
3
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 (Elmalt), for the water (Elwat) and for the maltosewater
interaction (Elmw) as well as the corresponding vanderWaals energy terms (LJ
malt, LJwat, and LJmw) 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
wb1 200ps
wb2 500ps
w 250ps
w35 200ps
w40 200ps
w60 950ps
va 500ps
vb 500ps
vc 500ps
Avg water
Avg wb
Avg vacuo
Tot
Std Slp
-14342 177
0
-14443 178 -129
-3741
74 nd
-3220
69
14
-2704
64
13
-1055
64
5
589
6
1
591
6
1
670
4
1
-6584
-14393
617
Kin
4279
4273
1201
1353
1559
2301
68
68
68
2494
4276
68
Pot
Bond EL-malt LJ -malt El-mw LJ -mw El-wat LJ -wat
-18621 127
573
-24
-420
-96 -21889 3109
-18717
46
572
-21
-424
-97 -21904 3111
-4942 123
492
-21
-401
-90
-5909
865
-4573 137
574
-20
-397
-88
-5556
777
-4263 148
573
-20
-371
-90
-5218
715
-3356 189
572
-18
-305
-93
-4303
601
522 120
420
-18
523 126
414
-16
602 139
480
-18
-9078 128
559
-21
-386
-92 -10797 1529
-18669
86
572
-22
-422
-96 -21896 3110
549 128
438
-17
4
Table SII:
Statistic of the cluster analysis of run w that used sine and cosine values of the ,
and both dihedral angles as parameters for the cluster definition. The
population (Pop) of the six clusters together with their average and angles, their
hydroxymethyl group orientation of the reducing (1) and the nonreducing (2)
glucose are listed. The last column contains the correlation coefficient (Cor) that
are calculated from correlating the vectors defined by the four dihedral angles ,
and 1,2.
Pop % P
806 32
597 24
564 23
283 11
184
7
66
3
-45
-22
-1
0
-13
-29
1 2
-39 gg-gt
-26 gg-tg
-2 gg-gt
-1 gg-gg
-10 gt-gt
-31 tg-gt
Cor
0.47
0.35
0.42
0.65
0.33
0.44
5
Table SIII:
Cluster statistics from a cluster analysis of MD simulation w60. The average (Avg)
and standard deviation (Std) of the and dihedral angles and the average total
energy (Etot) are tabulated for all 19 clusters. The clusters are sorted by the
conformation of the glucose rings. 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 Popu
E-tot
Pop
Glucose lation
%
Avg Std Avg Std kJ/mol
4C1 4C1
274 16
-66
8
-40 10
-1061
4C1 4C1
139
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
Sum
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
Sum
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
3655 38
-38 17 -18 22 -1055
1C4 1C4
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
Sum
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
Sum
119
1
60 17 181 33 -1050
6
Figure 1:
The conformational space of the glycosidic linkage dihedral angles
and occupied during MD simulation w60 at 600K displayed in all
four parts of the figures as hatched area. Overplotted in a thick
closed line, the conformational space is indicated for those
conformers that have A) 4C14C1 B) 4C11C4 C) 1C44C1 D)1C4
1C
4 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.
7