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Coarse-graining protein structures with local multivariate features from molecular dynamics.

Zhang Z, Wriggers W - J Phys Chem B (2008)

Bottom Line: This allows for an efficient implementation, but the sequential algorithm does not guarantee the optimal mutual correlation of the sequentially assigned features.Tests on MD trajectories of two biological systems, bacteriophage T4 lysozyme and myosin II motor domain S1, demonstrate that the new algorithm provides statistically reproducible results and describes functionally relevant dynamics.In addition to its use in structure classification, the proposed coarse-graining thus provides a localized measure of MD sampling efficiency.

View Article: PubMed Central - PubMed

Affiliation: School of Health Information Sciences, University of Texas Health Science Center at Houston, Houston, TX 77030, USA.

ABSTRACT
A multivariate statistical theory, local feature analysis (LFA), extracts functionally relevant domains from molecular dynamics (MD) trajectories. The LFA representations, like those of principal component analysis (PCA), are low dimensional and provide a reduced basis set for collective motions of simulated proteins, but the local features are sparsely distributed and spatially localized, in contrast to global PCA modes. One key problem in the assignment of local features is the coarse-graining of redundant LFA output functions by means of seed atoms. One can solve the combinatorial problem by adding seed atoms one after another to a growing set, minimizing a reconstruction error at each addition. This allows for an efficient implementation, but the sequential algorithm does not guarantee the optimal mutual correlation of the sequentially assigned features. Here, we present a novel coarse-graining algorithm for proteins that directly minimizes the mutual correlation of seed atoms by Monte Carlo (MC) simulations. Tests on MD trajectories of two biological systems, bacteriophage T4 lysozyme and myosin II motor domain S1, demonstrate that the new algorithm provides statistically reproducible results and describes functionally relevant dynamics. The well-known undersampling of large-scale motion by short MD simulations is apparent also in our model, but the new coarse-graining offers a major advantage over PCA; converged features are invariant across multiple windows of the trajectory, dividing the protein into converged regions and a smaller number of localized, undersampled regions. In addition to its use in structure classification, the proposed coarse-graining thus provides a localized measure of MD sampling efficiency.

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(a) Root-mean-square fluctuations (RMSF) of Cα atoms calculated from the MD simulation of T4L. The RMSF curve is divided into the eight local features (Table 1). Cα-1 (1−13, which means the local feature spans residues 1−13) black; Cα-22 (14−42) red; Cα-52 (43−62) green; Cα-71 (63−78) blue; Cα-90 (79−99) orange; Cα-109 (100−113) magenta; Cα-116 (114−136) brown; and Cα-159 (137−162) cyan. (b) Output correlations (eq 11) between the seed atoms and T4L as a function of residue number in the case of n = 8. Only the correlations between one seed atom and the atoms in its corresponding dynamic domain are plotted, which are colored according to the RMSF curve. The eight seed atoms are indicated by dots.
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fig3: (a) Root-mean-square fluctuations (RMSF) of Cα atoms calculated from the MD simulation of T4L. The RMSF curve is divided into the eight local features (Table 1). Cα-1 (1−13, which means the local feature spans residues 1−13) black; Cα-22 (14−42) red; Cα-52 (43−62) green; Cα-71 (63−78) blue; Cα-90 (79−99) orange; Cα-109 (100−113) magenta; Cα-116 (114−136) brown; and Cα-159 (137−162) cyan. (b) Output correlations (eq 11) between the seed atoms and T4L as a function of residue number in the case of n = 8. Only the correlations between one seed atom and the atoms in its corresponding dynamic domain are plotted, which are colored according to the RMSF curve. The eight seed atoms are indicated by dots.

Mentions: The seed atoms (3, 51, 108, 162) consistently found by CGLC are not redundant as was the case with SPA-0. Also, the even distribution is achieved without any artificial constraint, as was the case with SPA-50. We note that these four seed atoms correspond to the four most flexible regions in T4L (Figure 3a) as measured by the root-mean-square fluctuation (RMSF) of the Cα atoms.


Coarse-graining protein structures with local multivariate features from molecular dynamics.

Zhang Z, Wriggers W - J Phys Chem B (2008)

(a) Root-mean-square fluctuations (RMSF) of Cα atoms calculated from the MD simulation of T4L. The RMSF curve is divided into the eight local features (Table 1). Cα-1 (1−13, which means the local feature spans residues 1−13) black; Cα-22 (14−42) red; Cα-52 (43−62) green; Cα-71 (63−78) blue; Cα-90 (79−99) orange; Cα-109 (100−113) magenta; Cα-116 (114−136) brown; and Cα-159 (137−162) cyan. (b) Output correlations (eq 11) between the seed atoms and T4L as a function of residue number in the case of n = 8. Only the correlations between one seed atom and the atoms in its corresponding dynamic domain are plotted, which are colored according to the RMSF curve. The eight seed atoms are indicated by dots.
© Copyright Policy - open-access - ccc-price
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2651751&req=5

fig3: (a) Root-mean-square fluctuations (RMSF) of Cα atoms calculated from the MD simulation of T4L. The RMSF curve is divided into the eight local features (Table 1). Cα-1 (1−13, which means the local feature spans residues 1−13) black; Cα-22 (14−42) red; Cα-52 (43−62) green; Cα-71 (63−78) blue; Cα-90 (79−99) orange; Cα-109 (100−113) magenta; Cα-116 (114−136) brown; and Cα-159 (137−162) cyan. (b) Output correlations (eq 11) between the seed atoms and T4L as a function of residue number in the case of n = 8. Only the correlations between one seed atom and the atoms in its corresponding dynamic domain are plotted, which are colored according to the RMSF curve. The eight seed atoms are indicated by dots.
Mentions: The seed atoms (3, 51, 108, 162) consistently found by CGLC are not redundant as was the case with SPA-0. Also, the even distribution is achieved without any artificial constraint, as was the case with SPA-50. We note that these four seed atoms correspond to the four most flexible regions in T4L (Figure 3a) as measured by the root-mean-square fluctuation (RMSF) of the Cα atoms.

Bottom Line: This allows for an efficient implementation, but the sequential algorithm does not guarantee the optimal mutual correlation of the sequentially assigned features.Tests on MD trajectories of two biological systems, bacteriophage T4 lysozyme and myosin II motor domain S1, demonstrate that the new algorithm provides statistically reproducible results and describes functionally relevant dynamics.In addition to its use in structure classification, the proposed coarse-graining thus provides a localized measure of MD sampling efficiency.

View Article: PubMed Central - PubMed

Affiliation: School of Health Information Sciences, University of Texas Health Science Center at Houston, Houston, TX 77030, USA.

ABSTRACT
A multivariate statistical theory, local feature analysis (LFA), extracts functionally relevant domains from molecular dynamics (MD) trajectories. The LFA representations, like those of principal component analysis (PCA), are low dimensional and provide a reduced basis set for collective motions of simulated proteins, but the local features are sparsely distributed and spatially localized, in contrast to global PCA modes. One key problem in the assignment of local features is the coarse-graining of redundant LFA output functions by means of seed atoms. One can solve the combinatorial problem by adding seed atoms one after another to a growing set, minimizing a reconstruction error at each addition. This allows for an efficient implementation, but the sequential algorithm does not guarantee the optimal mutual correlation of the sequentially assigned features. Here, we present a novel coarse-graining algorithm for proteins that directly minimizes the mutual correlation of seed atoms by Monte Carlo (MC) simulations. Tests on MD trajectories of two biological systems, bacteriophage T4 lysozyme and myosin II motor domain S1, demonstrate that the new algorithm provides statistically reproducible results and describes functionally relevant dynamics. The well-known undersampling of large-scale motion by short MD simulations is apparent also in our model, but the new coarse-graining offers a major advantage over PCA; converged features are invariant across multiple windows of the trajectory, dividing the protein into converged regions and a smaller number of localized, undersampled regions. In addition to its use in structure classification, the proposed coarse-graining thus provides a localized measure of MD sampling efficiency.

Show MeSH
Related in: MedlinePlus