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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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Coarse-graining results of T4L using CGLC for n = 4. (a) Starting with the initial seed atom set (40, 51, 53, 109) from SPA-0. (b) Starting with the initial seed atom set (1, 51, 109, 162) from SPA-50. (c) Starting with the initial seed atom set (1, 2, 3, 4). (d) Starting with the initial seed atom set (159, 160, 161, 162). The seed atoms in the lowest-correlation set (3, 51, 108, 162) are indicated by black dots.
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fig2: Coarse-graining results of T4L using CGLC for n = 4. (a) Starting with the initial seed atom set (40, 51, 53, 109) from SPA-0. (b) Starting with the initial seed atom set (1, 51, 109, 162) from SPA-50. (c) Starting with the initial seed atom set (1, 2, 3, 4). (d) Starting with the initial seed atom set (159, 160, 161, 162). The seed atoms in the lowest-correlation set (3, 51, 108, 162) are indicated by black dots.

Mentions: As a preliminary test of CGLC, we started with the seed atom sets resulting from SPA-0 (Elcsc = 0.042) and SPA-50 (Elcsc = −0.135). As described in , we minimized the linear chain seed correlation Elcsc (eq 12) systematically. Both examples (Figure 2a,b) converge to the same seed set (3, 51, 108, 162), which is close to the SPA-50 result, reaching a seed correlation of −0.179. Furthermore, we used two extremely uneven distributed start sets (1, 2, 3, 4) and (159, 160, 161, 162), with high seed correlations of 0.099 and 0.059, respectively. Both sets quickly converged to the same solution (Figure 2c,d).


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

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

Coarse-graining results of T4L using CGLC for n = 4. (a) Starting with the initial seed atom set (40, 51, 53, 109) from SPA-0. (b) Starting with the initial seed atom set (1, 51, 109, 162) from SPA-50. (c) Starting with the initial seed atom set (1, 2, 3, 4). (d) Starting with the initial seed atom set (159, 160, 161, 162). The seed atoms in the lowest-correlation set (3, 51, 108, 162) are indicated by black dots.
© Copyright Policy - open-access - ccc-price
Related In: Results  -  Collection

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

fig2: Coarse-graining results of T4L using CGLC for n = 4. (a) Starting with the initial seed atom set (40, 51, 53, 109) from SPA-0. (b) Starting with the initial seed atom set (1, 51, 109, 162) from SPA-50. (c) Starting with the initial seed atom set (1, 2, 3, 4). (d) Starting with the initial seed atom set (159, 160, 161, 162). The seed atoms in the lowest-correlation set (3, 51, 108, 162) are indicated by black dots.
Mentions: As a preliminary test of CGLC, we started with the seed atom sets resulting from SPA-0 (Elcsc = 0.042) and SPA-50 (Elcsc = −0.135). As described in , we minimized the linear chain seed correlation Elcsc (eq 12) systematically. Both examples (Figure 2a,b) converge to the same seed set (3, 51, 108, 162), which is close to the SPA-50 result, reaching a seed correlation of −0.179. Furthermore, we used two extremely uneven distributed start sets (1, 2, 3, 4) and (159, 160, 161, 162), with high seed correlations of 0.099 and 0.059, respectively. Both sets quickly converged to the same solution (Figure 2c,d).

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