skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

Abstract

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniquesmore » may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.« less

Authors:
;  [1];  [2];  [3]
  1. Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544 (United States)
  2. Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544 (United States)
  3. Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Str. 3, 60438 Frankfurt am Main (Germany)
Publication Date:
OSTI Identifier:
22308394
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 141; Journal Issue: 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALANINES; DIFFUSION; FUZZY LOGIC; MARKOV PROCESS; MOLECULAR DYNAMICS METHOD; PEPTIDES; SIMULATION

Citation Formats

Nedialkova, Lilia V., Amat, Miguel A., Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de, and Hummer, Gerhard, E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de. Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions. United States: N. p., 2014. Web. doi:10.1063/1.4893963.
Nedialkova, Lilia V., Amat, Miguel A., Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de, & Hummer, Gerhard, E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de. Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions. United States. doi:10.1063/1.4893963.
Nedialkova, Lilia V., Amat, Miguel A., Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de, and Hummer, Gerhard, E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de. Sun . "Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions". United States. doi:10.1063/1.4893963.
@article{osti_22308394,
title = {Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions},
author = {Nedialkova, Lilia V. and Amat, Miguel A. and Kevrekidis, Ioannis G., E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de and Hummer, Gerhard, E-mail: yannis@princeton.edu, E-mail: gerhard.hummer@biophys.mpg.de},
abstractNote = {Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.},
doi = {10.1063/1.4893963},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 11,
volume = 141,
place = {United States},
year = {2014},
month = {9}
}