Robust Perron cluster analysis in conformation dynamics

By Peter Deuflhard, Marcus Weber. 2005

546 citations recorded by the source corpus.

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.

Subfields: Molecular Biology, Spectroscopy, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/14c68453adb8b690753baf07339913b355c52860

How researchers see this paper

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In Molecular Biology

1. Frank No'e
2. Hao Wu
3. Christof Schutte
4. Stefan Klus
5. John D. Chodera
6. Péter Koltai
7. Feliks Nuske
8. Gary Froyland

In Spectroscopy

1. Frank No'e
2. Hao Wu
3. G. de Fabritiis
4. Christof Schutte
5. Boaz Nadler
6. John D. Chodera
7. Gary Froyland
8. Ioannis G. Kevrekidis

In Statistics and Probability

1. Frank No'e
2. Boaz Nadler
3. Kathrin Padberg
4. Hao Wu
5. Feliks Nuske
6. Christof Schutte
7. Ronald R. Coifman
8. Stefan Klus

Citations in the corpus

• Data-Driven Model Reduction and Transfer Operator Approximation (2017, methodology): “We employ the PCCA+ algorithm [46, 47] to coarse grain all MSM states into two macrostates.”
• Identification of slow molecular order parameters for Markov model construction. (2013, background): “• The metastable states (often referred to as “free energy basins”—although we will avoid this term as it would imply the projection onto some pre-defined coordinate set), can be computed from the sign structure of the leading eigenfunctions [81, 22].”
• Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems (2008, methodology): “Our computational approach is closely related to the transfer operator approach [46], which also computes an approximation to the eigenfunctions of the FP operator [27], and to Perron cluster analysis [18, 19].”
• Markov state models of biomolecular conformational dynamics (2014, background): “The foundational work on coarse-graining MSMs was the development of PCCA [31] and PCCA+ [32].”