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 techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.
authors.affiliation: Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Lilia V
authors.initials: LV
authors.lastname: Nedialkova
authors.affiliation: Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Amat
authors.affiliation: Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Ioannis G
authors.initials: IG
authors.lastname: Kevrekidis
authors.affiliation: Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Str. 3, 60438 Frankfurt am Main, Germany.
authors.forename: Gerhard
authors.initials: G
authors.lastname: Hummer
mesh_terms: D016000:Cluster Analysis; D004058:Diffusion; D017143:Fuzzy Logic; D008390:Markov Chains; D056004:Molecular Dynamics Simulation; D010455:Peptides / Q000737:chemistry*; D017510:Protein Folding
chemical_list: D010455:Peptides