Maximum Margin Clustering for State Decomposition of Metastable Systems

Wu, Hao

doi:10.1007/978-3-642-38679-4_56

Cited by 3 publications

(4 citation statements)

References 38 publications

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“…Then the dual problem of (B.13) can be written as (E.4) θ = atan2 x (2) , x (1) and γ = 1.67. It is easy to verify that Model I and Model II are time-reversible diffusion processes, and their equilibrium distributions are π (x) ∝ exp (−U I (x)) and π (x) ∝ exp (−U II (x)) separately.…”

Section: Resultsmentioning

confidence: 99%

Maximum margin clustering for state decomposition of metastable systems

2015

Neurocomputing

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When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most popular and simplest approach is geometric clustering which is developed based on the classical clustering technique. However, the prerequisites of this approach are: (1) data are obtained from simulations or experiments which are in global equilibrium and (2) the coordinate system is appropriately selected. Recently, the kinetic clustering approach based on phase space discretization and transition probability estimation has drawn much attention due to its applicability to more general cases, but the choice of discretization policy is a difficult task. In this paper, a new decomposition method designated as maximum margin metastable clustering is proposed, which converts the problem of metastable state decomposition to a semi-supervised learning problem so that the large margin technique can be utilized to search for the optimal decomposition without phase space discretization. Moreover, several simulation examples are given to illustrate the effectiveness of the proposed method.

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Section: Resultsmentioning

confidence: 99%

Maximum margin clustering for state decomposition of metastable systems

2015

Neurocomputing

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“…In the past, the DBSCAN could only provide results in one resolution, however, our ML-DBSCAN can provide metastable states in many resolutions. Therefore, we anticipate that our ML-DBSCAN algorithm may greatly assist the core-set MSM analysis of protein dynamics 15,19,25 , especially on the studies of functional conformational changes of biomolecules [51][52][53][54][55][56] .…”

Section: Gpu Implementation Greatly Accelerated the Ml-dbscan Analysis Of MD Simulation Datasets Of Larger Peptide And Protein Systemsmentioning

confidence: 99%

“…These clustering algorithms are often used to generate conformational states in Markov State Models (MSMs) [14][15][16][17][18][19][20][21][22][23][24][25][26][27] to elucidate biomolecular dynamics. The limitation of most existing clustering algorithms, however, is their inability to be used directly to identify kinetically metastable states, as they are based on geometric similarity between pairs of protein conformations.…”

Section: Introductionmentioning

confidence: 99%

Multi-Level DBSCAN: A Hierarchical Density-Based Clustering Method for Analyzing Molecular Dynamics Simulation Trajectories

Cao

Vasquez

et al. 2021

Preprint

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Molecular Dynamic (MD) simulations have been extensively used as a powerful tool to investigate dynamics of biological molecules in recent decades. Generally, MD simulations generate high-dimensional data that is very hard to visualize and comprehend. As a result, clustering algorithms have been commonly used to reduce the dimensionality of MD data with the key benefit being their ability to reduce the dimensionality of MD data without prior knowledge of structural details or dynamic mechanisms. In this paper, we propose a new algorithm, the Multi-Level Density-Based Spatial Clustering of Applications with Noise (ML-DBSCAN), which combines the clustering results at different resolution of density levels to obtain the hierarchical structure of the free energy landscape and the metastable state assignment. At relatively low resolutions, the ML-DBSCAN can efficiently detect high population regions that contain all metastable states, while at higher resolutions, the ML-DBSCAN can find all metastable states and structural details of the free energy landscape. We demonstrate the powerfulness of the ML-DBSCAN in generating metastable states with a particle moving in a Mexican hat-like potential, and four peptide and protein examples are used to demonstrate how hierarchical structures of free energy landscapes can be found. Furthermore, we developed a GPU implementation of the ML-DBSCAN, which allows the algorithm to handle larger MD datasets and be up to two orders of magnitude faster than the CPU implementation. We demonstrate the power of the ML-DBSCAN on MD simulation datasets of five systems: a 2D-potential, alanine dipeptide, β-hairpin Tryptophan Zipper 2 (Trpzip2), Human Islet Amyloid Polypeptide (hIAPP), and Maltose Binding Protein (MBP). Our code is available at https://github.com/liusong299/ML-DBSCAN.

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“…Berg re-implemented PCCA+ with a fast Newton-type local optimization algorithm [11]. The implementation details of PCCA+ can be found in [12] and in Appendix D of [13]. In principle, the optimization problem to be solved has many local maxima.…”

Section: The Foundation Of Pcca+mentioning

confidence: 99%

Implications of PCCA+ in Molecular Simulation

Weber

2018

Computation

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Upon ligand binding or during chemical reactions the state of a molecular system changes in time. Usually we consider a finite set of (macro-) states of the system (e.g., 'bound' vs. 'unbound'), although the process itself takes place in a continuous space. In this context, the formula χ = XA connects the micro-dynamics of the molecular system to its macro-dynamics. χ can be understood as a clustering of micro-states of a molecular system into a few macro-states. X is a basis of an invariant subspace of a transfer operator describing the micro-dynamics of the system. The formula claims that there is an unknown linear relation A between these two objects. With the aid of this formula we can understand rebinding effects, the electron flux in pericyclic reactions, and systematic changes of binding rates in kinetic ITC experiments. We can also analyze sequential spectroscopy experiments and rare event systems more easily. This article provides an explanation of the formula and an overview of some of its consequences.Keywords: Robust Perron Cluster Analysis; membership function; invariant subspace. MSC: 60J22 The Foundation of PCCA+Molecular simulation is used as a tool to estimate thermodynamical properties. Moreover, it could be used for investigation of molecular processes and their time scales. In computational drug design, e.g., binding affinities of ligand-receptor systems are estimated. In this case, trajectories in a 3N-dimensional space Ω of molecular conformations (N is the number of atoms) are generated. They will be denoted as micro-states x ∈ Ω in the following. After simulation the micro-states are classified as "bound" or "unbound". This classification can be achieved by projecting the state space Ω onto a low number n of macro-states of the system. Spectral clustering algorithms are one possible method in this context. Robust Perron Cluster Analysis (PCCA+) turned out to be a commonly used practical tool for this algorithmic step [1].Conformation Dynamics has been established in the late 1990s. From molecular simulations [2] transition matrices P ∈ R m×m were derived. The entries of P represent conditional transition probabilities between pre-defined m subsets of the state space Ω of a molecular process. Today P would be denoted as Markov State Model. According to the transfer operator theory and PCCA [3] the eigenvectors of these matrices were studied in the early 2000s leading to an empirical observation [4] and Figure 1: Given a matrix X ∈ R m×n of the n m leading eigenvectors of the m × m-transition matrix P, the m rows of X -plotted as n-dimensional points -seem to always form an (n − 1)-simplex. Some of those m points are located at the vertices of the simplices, other points are located on the edges. The points which are located at the n vertices of these simplices represent the thermodynamically stable conformations of the molecular systems. Whereas, the points which are located on the edges of the simplices represent transition regions. In order to transform the (n − 1)-simplex σ 1 ...

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Maximum Margin Clustering for State Decomposition of Metastable Systems

Cited by 3 publications

References 38 publications

Maximum margin clustering for state decomposition of metastable systems

Maximum margin clustering for state decomposition of metastable systems

Multi-Level DBSCAN: A Hierarchical Density-Based Clustering Method for Analyzing Molecular Dynamics Simulation Trajectories

Implications of PCCA+ in Molecular Simulation

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