Robust Perron cluster analysis in conformation dynamics

Konrad-Zuse-Zentrum fuer Informationstechnik, Berlin D-14195, Germany
Linear Algebra and its Applications (Impact Factor: 0.98). 01/2003; 398:161-184. DOI: 10.1016/j.laa.2004.10.026

ABSTRACT The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.

  • [Show abstract] [Hide abstract]
    ABSTRACT: We present a new cycle-flow-based method for finding fuzzy partitions of weighted directed networks coming from time series data. We show that this method overcomes essential problems of most existing clustering approaches, which tend to ignore important directional information by considering only one-step, one-directional node connections. Our method introduces a novel measure of communication between nodes using multi-step, bidirectional transitions encoded by a cycle decomposition of the probability flow. Symmetric properties of this measure enable us to construct an undirected graph that captures the information flow of the original graph seen by the data and apply clustering methods designed for undirected graphs. Finally, we demonstrate our algorithm by analyzing earthquake time series data, which naturally induce (time-)directed networks. Copyright (C) EPLA, 2014
    EPL (Europhysics Letters) 12/2014; 108(6):68008. DOI:10.1209/0295-5075/108/68008 · 2.27 Impact Factor
  • Source
  • [Show abstract] [Hide abstract]
    ABSTRACT: The slow processes of molecular dynamics (MD) simulations-governed by dominant eigenvalues and eigenfunctions of MD propagators-contain essential information on structures of and transition rates between long-lived conformations. Existing approaches to this problem, including Markov state models and the variational approach, represent the dominant eigenfunctions as linear combinations of a set of basis functions. However the choice of the basis functions and their systematic statistical estimation are unsolved problems. Here, we propose a new class of kinetic models called Markov transition models (MTMs) that approximate the transition density of the MD propagator by a mixture of probability densities. Specifically, we use Gaussian MTMs where a Gaussian mixture model is used to approximate the symmetrized transition density. This approach allows for a direct computation of spectral components. In contrast with the other Galerkin-type approximations, our approach can automatically adjust the involved Gaussian basis functions and handle the statistical uncertainties in a Bayesian framework. We demonstrate by some simulation examples the effectiveness and accuracy of the proposed approach.

Preview (2 Sources)

1 Download
Available from