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

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Supplement To:

Parametrization of the GROMOS Force Field for

Oligosaccharides and Assessment of the Efficiency of

Molecular Dynamics Simulations

Karl-Heinz Ott

Karl-Heinz Ott1 1 _{and Bernd Meyer}_{and Bernd Meyer}22

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

30602, USA 30602, USA

Present Addresses: Present Addresses:

1) American Cyanamid Co., P.O. Box 400, Princeton, NJ 08543-0400, USA and 1) American Cyanamid Co., P.O. Box 400, Princeton, NJ 08543-0400, USA and 2) Institut für Organische Chemie, M.L. King Platz 6, 20146 Hamburg, 2) Institut für Organische Chemie, M.L. King Platz 6, 20146 Hamburg, Germany

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Cluster analysis:

A complete, hierarchical clustering algorithm

A complete, hierarchical clustering algorithm1,21,2_{was used to group the}_{was used to group the}

conformations that were represented by sine and cosine values of selected conformations that were represented by sine and cosine values of selected dihedral angles. For run w60, a four dimensional conformational space was dihedral angles. For run w60, a four dimensional conformational space was defined by the

defined by the ϕ and and ψ angles and by two intra-ring dihedral angles (O5-C1- angles and by two intra-ring dihedral angles (O5-C1-C2-C3) that are characteristic for the ring conformations. The statistical data C2-C3) that are characteristic for the ring conformations. The statistical data analysis package BLSS

analysis package BLSS33_{was used to generate the cluster tree for the}_{was used to generate the cluster tree for the}

conformations observed in 300 fs intervals. The resulting cluster tree was conformations observed in 300 fs intervals. The resulting cluster tree was analyzed statistically and an appropriate cutting level was chosen. The analyzed statistically and an appropriate cutting level was chosen. The remaining conformations, sampled in 100 fs steps, were sorted into the remaining conformations, sampled in 100 fs steps, were sorted into the nearest cluster. Conformations that differed by more than 1.5 times the nearest cluster. Conformations that differed by more than 1.5 times the standard deviations from the cluster definitions were rejected. The same standard deviations from the cluster definitions were rejected. The same procedure but with the

procedure but with the ϕ,, ψ, and the both , and the both ω angles as parameters for the angles as parameters for the clustering was used to classify the results of the other MD simulations of this clustering was used to classify the results of the other MD simulations of this work (data only shown for run w).

work (data only shown for run w). 1

1 J.A. Hartigan, Clustering Algorithms,J.A. Hartigan, Clustering Algorithms, Wiley, New York, 1975. Wiley, New York, 1975. 2

2 B.Everitt, Cluster AnalysisB.Everitt, Cluster Analysis, Halsted, New York, 1980., Halsted, New York, 1980. 3

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

System, Norton, NY 1988. Norton, NY 1988.

Run w

The data set was split into 6 clusters, each having a correlation 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). 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

The highest populated cluster with a population of 32% has a gggg

conformation in the reducing ring and a

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

ring with the glycosidic linkage at ≈ -40-40oo_//-40_-40oo_{. Another highly populated}_{. Another highly populated}

cluster with 22% population has the same conformations of the cluster with 22% population has the same conformations of the hydroxymethyl groups but has

hydroxymethyl groups but has ϕ and and ψ at at ≈ 0 0oo_{. The same glycosidic linkage}_{. The same glycosidic linkage}

conformation with both hydroxymethyl groups in a

conformation with both hydroxymethyl groups in a gg gg conformation is foundconformation is found in another cluster with 11% population. 24% of the conformations form a in another cluster with 11% population. 24% of the conformations form a cluster that has average

cluster that has average ϕ and and ψ angles of angles of ≈ -30 -30oo_{which are the angles found}_{which are the angles found}

in X-ray crystal studies (F. Takusagawa and G.A. Jacobson,

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

213. 1978). In this cluster the ω angles are oriented in the angles are oriented in the gggg and the and the tgtg position for the reducing and the nonreducing residue, respectively (cf. Tab. position for the reducing and the nonreducing residue, respectively (cf. Tab. SII). A cluster with 7.5% of the total population has both

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a

a gtgt conformation. The glycosidic linkage of this cluster is characterized by conformation. The glycosidic linkage of this cluster is characterized by

ϕ//ψ values of values of ≈ -10-10oo_..

As is evident from the populations of the hydroxymethyl groups, the MD 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 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 populations of different minima, which is even true for the most populated minima.

minima.

Run w60

The cluster analysis resulted in 19 clusters (Tab. SIII). Based on the The cluster analysis resulted in 19 clusters (Tab. SIII). Based on the analysis of the transition rates between the clusters four major groups of analysis of the transition rates between the clusters four major groups of clusters can be identified (cf. Tab. SIII). They are characterized by the clusters can be identified (cf. Tab. SIII). They are characterized by the differences in the conformations of the glucose rings and have the glycosidic differences in the conformations of the glucose rings and have the glycosidic linkage in conformations close to the global minimum. Only 18% of the linkage in conformations close to the global minimum. Only 18% of the conformers have both hexose rings in the

conformers have both hexose rings in the 44_C_C 1

1 orientation. In 64% of the orientation. In 64% of the

simulation either the reducing or the nonreducing ring has the inverted simulation either the reducing or the nonreducing ring has the inverted 11_C_C

4 4

ring conformation. In 17% of the simulation both rings adopted the ring conformation. In 17% of the simulation both rings adopted the 11_C_C

4 4

conformation. conformation.

The cluster analysis revealed that the accessible range of the glycosidic The cluster analysis revealed that the accessible range of the glycosidic linkage space is significantly dependent on the ring conformations. linkage space is significantly dependent on the ring conformations. 44_C_C₁₁

conformers restrict the conformational flexibility of the glycosidic linkage conformers restrict the conformational flexibility of the glycosidic linkage compared to the

compared to the 11_C_C₄₄_{conformers. The strongest effect is found when}_{conformers. The strongest effect is found when}

comparing the conformational space accessible to the

comparing the conformational space accessible to the 11_C_C₄₄_--11_C_C₄₄_{species with}_{species with}

that of the

that of the 44_C_C₁₁_--44_C_C₁₁_{species (Fig. 1a,d). The position and size of the global}_{species (Fig. 1a,d). The position and size of the global}

minimum of the

minimum of the 44_C_C₁₁_--44_C_C₁₁_{conformers is similar to those found in the}_{conformers is similar to those found in the}

previously described calculations at 350K and 400K. The additional previously described calculations at 350K and 400K. The additional conformational flexibility apparent from the conformational space totally conformational flexibility apparent from the conformational space totally accesses at 600K (Fig. 1, hatched area) originates from a glucose in an accesses at 600K (Fig. 1, hatched area) originates from a glucose in an inverted

inverted 11_C_C₄₄_{conformation (Fig. 1b-d). When the nonreducing residue is in a}_{conformation (Fig. 1b-d). When the nonreducing residue is in a} 1

1_C_C₄₄_{conformation, the}_{conformation, the}_ϕ/ψ_{contour extends to more negative}_{contour extends to more negative}_ϕ_{angles (Fig.}_{angles (Fig.}

1b). In contrary, when the reducing residue adopts a

1b). In contrary, when the reducing residue adopts a 11_C_C₄₄_{conformation and}_{conformation and}

the nonreducing residue has the

the nonreducing residue has the 44_C_C₁₁_{conformation the}_{conformation the}_ϕ/ψ_{contours extend to}_{contours extend to}

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

in the 11_C_C₄₄_{conformation, the}_{conformation, the}_ϕ/ψ_{contour shows the increased flexibility to}_{contour shows the increased flexibility to}

more negative

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while the hexose ring conformations are both in

while the hexose ring conformations are both in 44_C_C₁₁_{. Some of the conformers}_{. Some of the conformers}

with

with ψ around 180 around 180oo_{are found during the time of conformational transitions}_{are found during the time of conformational transitions}

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[image:5.612.83.467.339.455.2]

Table S I: Table S I:

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

the MD simulations, wb1, wb2, w, w35, w40, w60 and the in vacuoin vacuo MD MD simulations. Additionally, the total kinetic energy (Kin) the total potential simulations. Additionally, the total kinetic energy (Kin) the total potential Energy (Pot), the electrostatic energy terms for the maltose (El-malt), for the 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 water (El-wat) and for the maltose-water interaction (El-mw) as well as the corresponding van

corresponding van-der-der-Waals energy terms (LJ-malt, LJ-wat, and LJ-mw) are-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). 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), The average energy terms for the six MD simulations in water (AVG water), and for the three

and for the three in vacuoin vacuo MD simulations (AVG vacuo) are also displayed. MD simulations (AVG vacuo) are also displayed. ND: not determined.

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

va 500ps 589 6 1 68 522 120 420 -18 vb 500ps 591 6 1 68 523 126 414 -16 vc 500ps 670 4 1 68 602 139 480 -18

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Table SII: Table SII:

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

the ϕ, , ψ and both and both ω dihedral angles as parameters for the cluster definition. dihedral angles as parameters for the cluster definition. The population (Pop) of the six clusters together with their average

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

angles, their hydroxymethyl group orientation of the reducing (

angles, their hydroxymethyl group orientation of the reducing (ω₁₁) and the) and the nonreducing (

nonreducing (ω₂₂) glucose are listed. The last column contains the correlation) glucose are listed. The last column contains the correlation coefficient (Cor) that are calculated from correlating the vectors defined by coefficient (Cor) that are calculated from correlating the vectors defined by the four dihedral angles

the four dihedral angles ϕ, , ψ and and ω_1,2_1,2..

Pop % P ϕ ψ ω1−ω2 Cor

806 32 -45 -39 gg-gt 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

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[image:7.612.85.291.228.468.2]

Table SIII: Table SIII:

Cluster statistics from a cluster analysis of MD simulation w60. The average Cluster statistics from a cluster analysis of MD simulation w60. The average (Avg) and standard deviation (Std) of the

(Avg) and standard deviation (Std) of the ϕ and and ψ dihedral angles and the dihedral angles and the average total energy (E-tot) are tabulated for all 19 clusters. The clusters are average total energy (E-tot) are tabulated for all 19 clusters. The clusters are sorted by the conformation of the glucose rings. Clusters representing sorted by the conformation of the glucose rings. Clusters representing inverted glycosidic linkage conformations are listed separately at the bottom inverted glycosidic linkage conformations are listed separately at the bottom of the table. For each group, the total population and the group averages and of the table. For each group, the total population and the group averages and standard deviations are added in bold font (Sum).

standard deviations are added in bold font (Sum).

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AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA A A A A A A A A A A A A A A A A A A A A A A A AAAA AAAA AAAA A A A AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA

-180

-90

0

90

180

-180

-90

0

90

180

ϕϕ

ψ

AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AA AAAA AAAA AAAA A A A AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA 10 10 50 10

-180

-90

0

90

180

-180

-90

0

90

180

ϕϕ

ψ

AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA A A A A A A A A A A A A A A A A A A A A A A A AAAA AAAA AAAA A A A AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA 10 50 10

-180

-90

0

90

180

-180

-90

0

90

180

ϕϕ

ψ

AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA A A A A A A A A A A A A A A A A A A A A A A A AAAA AAAA AAAA A A A AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA AAAA 10 10 10 10 10 10 50 10 10

-180

-90

0

90

180

-180

-90

0

90

180

ϕϕ

ψ

A

B

C

D

[image:8.612.104.514.105.489.2]

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Figure 1:

Figure 1: The conformational space of the glycosidic linkage dihedralThe conformational space of the glycosidic linkage dihedral angles

angles ϕ and and ψ occupied during MD simulation w60 at 600K occupied during MD simulation w60 at 600K displayed in all four parts of the figures as hatched area. displayed in all four parts of the figures as hatched area. Overplotted in a thick closed line, the conformational space is Overplotted in a thick closed line, the conformational space is indicated for those conformers that have A)

indicated for those conformers that have A) 44_C_C₁₁_--44_C_C₁₁_B)_B) 4

4_C_C₁₁_--11_C_C₄₄_C)_C)11_C_C₄₄_--44_C_C₁₁_D)_D)11_C_C₄₄_--11_C_C₄₄_{conformations of the reducing}_{conformations of the reducing}

and the nonreducing glucose's, respectively. Lowest contours and the nonreducing glucose's, respectively. Lowest contours and area boundaries are drawn at 10 percent of the height of and area boundaries are drawn at 10 percent of the height of the highest populated bin.