Identifying Metastable States of Folding Proteins

Jain, Abhinav; Stock, Gerhard

doi:10.1021/ct300077q

Cited by 77 publications

(120 citation statements)

References 46 publications

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“…72 First, the k-means geometric clustering algorithm 73 is used in an unsupervised manner to reduce the large number of MD snapshots (∼10 6 -10 7 ) to a manageable number of microstates (∼10 3 -10 4 ). The resulting microstates can then be merged into metastable states using the most probable path algorithm, assuming a time-scale separation between the fast intrastate motion within the metastable states and slow interstate transitions.…”

Section: E Most Probable Path Clusteringmentioning

confidence: 99%

Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates

Sittel

Jain

Stock

2014

The Journal of Chemical Physics

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207

173

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Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional free energy landscape. Using Cartesian coordinates, first the translation and overall rotation need to be removed from the trajectory. Since the rotation depends via the moment of inertia on the molecule's structure, this separation is only straightforward for relatively rigid systems. Adopting millisecond molecular dynamics simulations of the folding of villin headpiece and the functional dynamics of BPTI provided by D. E. Shaw Research, it is demonstrated via a comparison of local and global rotational fitting that the structural dynamics of flexible molecules necessarily results in a mixing of overall and internal motion. Even for the small-amplitude functional motion of BPTI, the conformational distribution obtained from a Cartesian principal component analysis therefore reflects to some extend the dominant overall motion rather than the much smaller internal motion of the protein. Internal coordinates such as backbone dihedral angles, on the other hand, are found to yield correct and well-resolved energy landscapes for both examples. The virtues and shortcomings of the choice of various fitting schemes and coordinate sets as well as the generality of these results are discussed in some detail.

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Section: E Most Probable Path Clusteringmentioning

confidence: 99%

Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates

Sittel

Jain

Stock

2014

The Journal of Chemical Physics

Self Cite

207

173

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“…In [27], a singular value decomposition based lumping algorithm for nonreversible systems was proposed. Furthermore, Jain and Stock [28] presented a "most probable path algorithm" for bin lumping in order to avoid the computation of large matrix decompositions, and a Bayesian lumping method was proposed in [29] which considers the statistical uncertainty in transition probabilities. The main difficulty of kinetic clustering comes from the choice of bins, and the boundaries of metastable states are unable to be accurately captured with a poor choice of bins.…”

Section: Introductionmentioning

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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“…A number of methods have now been proposed to deal with these issues [28][29][30][31]. For example, we previously presented the super-level-set hierarchical clustering (SHC) algorithm [28], which was inspired by recent developments in topological model construction.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Nyström methods for constructing Markov state models for conformational dynamics

Yao

Cui

Bowman

et al. 2013

The Journal of Chemical Physics

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Markov state models (MSMs) have become a popular approach for investigating the conformational dynamics of proteins and other biomolecules. MSMs are typically built from numerous molecular dynamics simulations by dividing the sampled configurations into a large number of microstates based on geometric criteria. The resulting microstate model can then be coarsegrained into a more understandable macro state model by lumping together rapidly mixing microstates into larger, metastable aggregates. However, finite sampling often results in the creation of many poorly sampled microstates. During coarse-graining, these states are mistakenly identified as being kinetically important because transitions to/from them appear to be slow.In this paper we propose a formalism based on an algebraic principle for matrix approximation, i.e. the Nyström method, to deal with such poorly sampled microstates. Our scheme builds a hierarchy of microstates from high to low populations and progressively applies spectral clustering on sets of microstates within each level of the hierarchy. It helps spectral clustering identify metastable aggregates with highly populated microstates rather than being distracted by lowly populated states. We demonstrate the ability of this algorithm to discover the major metastable states on two model systems, the alanine dipeptide and trpzip2 peptide.

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Identifying Metastable States of Folding Proteins

Cited by 77 publications

References 46 publications

Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates

Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates

Maximum margin clustering for state decomposition of metastable systems

Hierarchical Nyström methods for constructing Markov state models for conformational dynamics

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