Computer Science

Euclidean sections of protein conformation space and their implications in dimensionality reduction

Document Type

Article

Abstract

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality-reduction methods using the pairwise root-mean-square deviation (RMSD) as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality-reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N-dimensional Euclidean space R3N. We formally define the protein conformation space as the quotient space of R3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise RMSD is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean-based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra-peptide and β-hairpin systems.

Publication Title

Proteins: Structure, Function and Bioinformatics

Publication Date

2014

Volume

82

Issue

10

First Page

2585

Last Page

2596

ISSN

0887-3585

DOI

10.1002/prot.24622

Keywords

dimensionality reduction, free energy landscape, isomap, principal component analysis, protein conformation space

APA Citation

Duan, M., Li, M., Han, L., & Huo, S. (2014). Euclidean sections of protein conformation space and their implications in dimensionality reduction. Proteins: Structure, Function, and Bioinformatics, 82(10), 2585-2596.

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