Robust Density-Based Clustering To Identify Metastable Conformational States of Proteins

Sittel, Florian; Stock, Gerhard

doi:10.1021/acs.jctc.5b01233

Cited by 81 publications

(165 citation statements)

References 42 publications

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“…The color of each state denotes the value of the committor-the probability of reaching the helix state before returning to the coil state. studied by Stock and coworkers, 43,52,61 as a reference in order to assess to what extent CG models are capable of reproducing the kinetic properties of this more detailed model. We note that it is well-known that distinct AA force fields yield widely varying results, e.g., in terms of helical propensities, for short peptide systems.…”

Section: Resultsmentioning

confidence: 99%

“…A density clustering algorithm was then applied to the five "most significant" dimensions in order to determine the number and placement of microstates, following previous investigation of the AA trajectory. 52 This procedure yields 32 states in all cases, corresponding to the enumeration of all possible helical/coil state combinations for each of the 5 peptide bonds. As described further in the Supporting Information section, the helical (h) and coil (c) states for individual peptide bonds roughly correspond to the α and β regions, respectively, of the corresponding Ramachandran plot.…”

Section: Markov State Modelsmentioning

confidence: 99%

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Structural-Kinetic-Thermodynamic Relationships Identified from Physics-based Molecular Simulation Models

Rudzinski

Bereau

2017

Preprint

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Coarse-grained molecular simulation models have provided immense, often general, insight into the complex behavior of condensed-phase systems, but suffer from a lost connection to the true dynamical properties of the underlying system. In general, the physics that is built into a model shapes the free-energy landscape, restricting the attainable static and kinetic properties. In this work, we perform a detailed investigation into the property interrelationships resulting from these restrictions, for a representative system of the helix-coil transition. Inspired by high-throughput studies, we systematically vary force-field parameters and monitor their structural, kinetic, and thermodynamic properties. The focus of our investigation is a simple coarse-grained model, which accurately represents the underlying structural ensemble, i.e., effectively avoids sterically-forbidden configurations. As a result of this built-in physics, we observe a rather large restriction in the topology of the networks characterizing the simulation kinetics. When screening across force-field parameters, we find that structurally-accurate models also best reproduce the kinetics, suggesting structural-kinetic relationships for these models. Additionally, an investigation into thermodynamic properties reveals a link between the cooperativity of the transition and the network topology at a single reference temperature.

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Section: Resultsmentioning

confidence: 99%

Section: Markov State Modelsmentioning

confidence: 99%

Structural-Kinetic-Thermodynamic Relationships Identified from Physics-based Molecular Simulation Models

Rudzinski

Bereau

2017

Preprint

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“…29,118,119 That is, it is difficult to separate out overall and internal motion of biopolymers when using Cartesian coordinates. 29 However, the selection of an internal coordinate requires some prior knowledge about the system, or introduces bias based on some assumption about the system. Therefore, we assume the philosophical position of maximal ignorance and select Cartesian coordinates as features for testing HDBSCAN and Amorim–Hennig as first-pass clustering techniques for MD data.…”

Section: Methodsmentioning

confidence: 99%

Uncovering Large-Scale Conformational Change in Molecular Dynamics without Prior Knowledge

Melvin

Godwin

Xiao

et al. 2016

J. Chem. Theory Comput.

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As the length of molecular dynamics (MD) trajectories grows with increasing computational power, so does the importance of clustering methods for partitioning trajectories into conformational bins. Of the methods available, the vast majority require users to either have some a priori knowledge about the system to be clustered or to tune clustering parameters through trial and error. Here we present non-parametric uses of two modern clustering techniques suitable for first-pass investigation of an MD trajectory. Being non-parametric, these methods require neither prior knowledge nor parameter tuning. The first method, HDBSCAN, is fast—relative to other popular clustering methods—and is able to group unstructured or intrinsically disordered systems (such as intrinsically disordered proteins, or IDPs) into bins that represent global conformational shifts. HDBSCAN is also useful for determining the overall stability of a system—as it tends to group stable systems into one or two bins—and identifying transition events between metastable states. The second method, iMWK-Means, with explicit rescaling followed by K-Means, while slower than HDBSCAN, performs well with stable, structured systems such as folded proteins and is able to identify higher resolution details such as changes in relative position of secondary structural elements. Used in conjunction, these clustering methods allow a user to discern quickly and without prior knowledge the stability of a simulated system and identify both local and global conformational changes.

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“…The robust density clustering 10 The number of components, and thus number of clusters, is chosen with BIC 17,18 .…”

Section: Robust Density Clusteringmentioning

confidence: 99%

InfleCS: Clustering Free Energy Landscapes with Gaussian Mixtures

Westerlund

Delemotte

2019

J. Chem. Theory Comput.

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Free energy landscapes provide insights into conformational ensembles of biomolecules.In order to analyze these landscapes and elucidate mechanisms underlying conformational changes, there is a need to extract metastable states with limited noise. This has remained a formidable task, despite a plethora of existing clustering methods.We present InfleCS, a novel method for extracting well-defined core states from free energy landscapes. The method is based on a Gaussian mixture free energy estimator and exploits the shape of the estimated density landscape. The core states that naturally arise from the clustering allow for detailed characterization of the conformational ensemble. The clustering quality is evaluated on three toy models with different properties, where the method is shown to consistently outperform other conventional and state-of-the-art clustering methods. Finally, the method is applied to a temperature enhanced molecular dynamics simulation of Ca 2+ -bound Calmodulin. Through the free energy landscape, we discover a pathway between a canonical and a compact state, revealing conformational changes driven by electrostatic interactions. arXiv:1905.03110v2 [physics.bio-ph] 30 Oct 2019Gaussian mixture models provide accurate estimates of free energy landscapes 1 . Determining metastable core states within a protein's free energy landscape is key to obtaining important biological insights. However, extracting such states from molecular dynamics (MD) simulations with conventional clustering methods is far from straightforward.First of all, we are interested in the metastable configurations at free energy minima, the so-called core states. Since proteins move continuously as they explore free energy landscapes, it is difficult to assess an exact state boundary. Moreover, configurations on transition pathways between metastable states generally contribute to noise when characterizing these states. On top of this, the original data is high dimensional, and the necessary dimensionality reduction results in poorly separated states. Finally, the number of metastable core states is typically not known a priori. Thus, to robustly characterize states without any knowledge of the conformational ensemble, we need a clustering method that is solely based on the data.Many popular clustering methods are based on simple geometric criteria 2-5 . K-means and agglomerative-Ward, for example, attempt to minimize the within-cluster variance. They work very well on datasets with well-separated spherical clusters, but fail when these assumptions are not met. Spectral clustering 6 , on the other hand, can accurately assign labels to nonconvex clusters by performing spectral embedding prior to K-means clustering. The spectral embedding involves learning the data manifold using local neighborhoods around data points.In general, geometric clustering methods assign labels to all points and may not accurately identify the boundary between states at the free energy barrier, which leads to noisy state definitions. An idea is to use th...

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Robust Density-Based Clustering To Identify Metastable Conformational States of Proteins

Cited by 81 publications

References 42 publications

Structural-Kinetic-Thermodynamic Relationships Identified from Physics-based Molecular Simulation Models

Structural-Kinetic-Thermodynamic Relationships Identified from Physics-based Molecular Simulation Models

Uncovering Large-Scale Conformational Change in Molecular Dynamics without Prior Knowledge

InfleCS: Clustering Free Energy Landscapes with Gaussian Mixtures

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