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Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models.

Na H, Jernigan RL, Song G - PLoS Comput. Biol. (2015)

Bottom Line: For this reason, coarse-grained models have been used successfully.The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes.The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, Iowa State University, Ames, Iowa, United States of America.

ABSTRACT
Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations--how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

No MeSH data available.


Illustration of how the sparseness of the Hessian matrix can be maintained throughout the iterative matrix projection procedure, when coarse-graining is performed by selecting the Cα atoms for retention.(A) In the first step the original Hessian matrix is shuffled so that Cα atoms (in dark gray at the top-left corner) are separated from the non-Cα atoms (in light gray). Blue dots represent non-zero elements. (B) In the second step the non-Cα atoms are rearranged again so that those interacting with one another are placed close together in the matrix using, for example, the Cuthill-McKee algorithm [54]. As a result, most non-zero elements are placed near the diagonal. (C) Matrix after performing one projection to remove atoms in group r. The red dots represent the blocks modified by the projection. The sparseness of the non-Cα region is mostly unaffected. The sparseness of the white region (interactions with Cα atoms) can be maintained by using an appropriate threshold value ξ, see text.
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pcbi.1004542.g001: Illustration of how the sparseness of the Hessian matrix can be maintained throughout the iterative matrix projection procedure, when coarse-graining is performed by selecting the Cα atoms for retention.(A) In the first step the original Hessian matrix is shuffled so that Cα atoms (in dark gray at the top-left corner) are separated from the non-Cα atoms (in light gray). Blue dots represent non-zero elements. (B) In the second step the non-Cα atoms are rearranged again so that those interacting with one another are placed close together in the matrix using, for example, the Cuthill-McKee algorithm [54]. As a result, most non-zero elements are placed near the diagonal. (C) Matrix after performing one projection to remove atoms in group r. The red dots represent the blocks modified by the projection. The sparseness of the non-Cα region is mostly unaffected. The sparseness of the white region (interactions with Cα atoms) can be maintained by using an appropriate threshold value ξ, see text.

Mentions: Fig 1 illustrates how the sparseness of the Hessian matrix is maintained throughout the iterative matrix projection procedure. At the initial step, atoms are shuffled so that Cα atoms are grouped together and placed on the left-most side of the Hessian matrix, as shown in Fig 1(A), where the grouped Cα and non-Cα atoms are represented by dark and light gray blocks, respectively. Blue dots represent the non-zero elements of the Hessian matrix. The non-Cα atoms can then be further rearranged, for example, using the Cuthill-McKee algorithm [54], so that the atoms that interact with one another are placed close together in the matrix. As a result, the non-zero elements are relocated near the diagonal of the matrix (see Fig 1(B)). In such a sparse matrix, Fig 1(C) shows the effect of applying one matrix projection using Eq (4), where the red dots represent the elements of the matrix whose values are modified. Note that the sparseness of the non-Cα region is mostly unaffected by the projection. The sparseness of the white region (interactions with Cα atoms) can be maintained by using an appropriate threshold value ξ mentioned earlier.


Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models.

Na H, Jernigan RL, Song G - PLoS Comput. Biol. (2015)

Illustration of how the sparseness of the Hessian matrix can be maintained throughout the iterative matrix projection procedure, when coarse-graining is performed by selecting the Cα atoms for retention.(A) In the first step the original Hessian matrix is shuffled so that Cα atoms (in dark gray at the top-left corner) are separated from the non-Cα atoms (in light gray). Blue dots represent non-zero elements. (B) In the second step the non-Cα atoms are rearranged again so that those interacting with one another are placed close together in the matrix using, for example, the Cuthill-McKee algorithm [54]. As a result, most non-zero elements are placed near the diagonal. (C) Matrix after performing one projection to remove atoms in group r. The red dots represent the blocks modified by the projection. The sparseness of the non-Cα region is mostly unaffected. The sparseness of the white region (interactions with Cα atoms) can be maintained by using an appropriate threshold value ξ, see text.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4608564&req=5

pcbi.1004542.g001: Illustration of how the sparseness of the Hessian matrix can be maintained throughout the iterative matrix projection procedure, when coarse-graining is performed by selecting the Cα atoms for retention.(A) In the first step the original Hessian matrix is shuffled so that Cα atoms (in dark gray at the top-left corner) are separated from the non-Cα atoms (in light gray). Blue dots represent non-zero elements. (B) In the second step the non-Cα atoms are rearranged again so that those interacting with one another are placed close together in the matrix using, for example, the Cuthill-McKee algorithm [54]. As a result, most non-zero elements are placed near the diagonal. (C) Matrix after performing one projection to remove atoms in group r. The red dots represent the blocks modified by the projection. The sparseness of the non-Cα region is mostly unaffected. The sparseness of the white region (interactions with Cα atoms) can be maintained by using an appropriate threshold value ξ, see text.
Mentions: Fig 1 illustrates how the sparseness of the Hessian matrix is maintained throughout the iterative matrix projection procedure. At the initial step, atoms are shuffled so that Cα atoms are grouped together and placed on the left-most side of the Hessian matrix, as shown in Fig 1(A), where the grouped Cα and non-Cα atoms are represented by dark and light gray blocks, respectively. Blue dots represent the non-zero elements of the Hessian matrix. The non-Cα atoms can then be further rearranged, for example, using the Cuthill-McKee algorithm [54], so that the atoms that interact with one another are placed close together in the matrix. As a result, the non-zero elements are relocated near the diagonal of the matrix (see Fig 1(B)). In such a sparse matrix, Fig 1(C) shows the effect of applying one matrix projection using Eq (4), where the red dots represent the elements of the matrix whose values are modified. Note that the sparseness of the non-Cα region is mostly unaffected by the projection. The sparseness of the white region (interactions with Cα atoms) can be maintained by using an appropriate threshold value ξ mentioned earlier.

Bottom Line: For this reason, coarse-grained models have been used successfully.The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes.The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, Iowa State University, Ames, Iowa, United States of America.

ABSTRACT
Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations--how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

No MeSH data available.