29,988 research outputs found
Conformational and functional analysis of molecular dynamics trajectories by Self-Organising Maps
<p>Abstract</p> <p>Background</p> <p>Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.</p> <p>Results</p> <p>The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.</p> <p>Conclusions</p> <p>The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.</p
Graph Theory and Networks in Biology
In this paper, we present a survey of the use of graph theoretical techniques
in Biology. In particular, we discuss recent work on identifying and modelling
the structure of bio-molecular networks, as well as the application of
centrality measures to interaction networks and research on the hierarchical
structure of such networks and network motifs. Work on the link between
structural network properties and dynamics is also described, with emphasis on
synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
Simultaneous Coherent Structure Coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity
The clustering of data into physically meaningful subsets often requires
assumptions regarding the number, size, or shape of the subgroups. Here, we
present a new method, simultaneous coherent structure coloring (sCSC), which
accomplishes the task of unsupervised clustering without a priori guidance
regarding the underlying structure of the data. sCSC performs a sequence of
binary splittings on the dataset such that the most dissimilar data points are
required to be in separate clusters. To achieve this, we obtain a set of
orthogonal coordinates along which dissimilarity in the dataset is maximized
from a generalized eigenvalue problem based on the pairwise dissimilarity
between the data points to be clustered. This sequence of bifurcations produces
a binary tree representation of the system, from which the number of clusters
in the data and their interrelationships naturally emerge. To illustrate the
effectiveness of the method in the absence of a priori assumptions, we apply it
to three exemplary problems in fluid dynamics. Then, we illustrate its capacity
for interpretability using a high-dimensional protein folding simulation
dataset. While we restrict our examples to dynamical physical systems in this
work, we anticipate straightforward translation to other fields where existing
analysis tools require ad hoc assumptions on the data structure, lack the
interpretability of the present method, or in which the underlying processes
are less accessible, such as genomics and neuroscience
Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways
Diverse classes of proteins function through large-scale conformational
changes; sophisticated enhanced sampling methods have been proposed to generate
these macromolecular transition paths. As such paths are curves in a
high-dimensional space, they have been difficult to compare quantitatively, a
prerequisite to, for instance, assess the quality of different sampling
algorithms. The Path Similarity Analysis (PSA) approach alleviates these
difficulties by utilizing the full information in 3N-dimensional trajectories
in configuration space. PSA employs the Hausdorff or Fr\'echet path
metrics---adopted from computational geometry---enabling us to quantify path
(dis)similarity, while the new concept of a Hausdorff-pair map permits the
extraction of atomic-scale determinants responsible for path differences.
Combined with clustering techniques, PSA facilitates the comparison of many
paths, including collections of transition ensembles. We use the closed-to-open
transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for
the assessment enhanced sampling algorithms---to examine multiple microsecond
equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free
form alongside transition ensembles from the MD-based dynamic importance
sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting
algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for
instance, that differences in DIMS-MD and FRODA paths were mediated by a set of
conserved salt bridges whose charge-charge interactions are fully modeled in
DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis
methods relying on pre-defined collective variables, such as native contacts or
geometric quantities, can be used synergistically with PSA, as well as the
application of PSA to more complex systems such as membrane transporter
proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information
includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also
available from journal site
A self-learning algorithm for biased molecular dynamics
A new self-learning algorithm for accelerated dynamics, reconnaissance
metadynamics, is proposed that is able to work with a very large number of
collective coordinates. Acceleration of the dynamics is achieved by
constructing a bias potential in terms of a patchwork of one-dimensional,
locally valid collective coordinates. These collective coordinates are obtained
from trajectory analyses so that they adapt to any new features encountered
during the simulation. We show how this methodology can be used to enhance
sampling in real chemical systems citing examples both from the physics of
clusters and from the biological sciences.Comment: 6 pages, 5 figures + 9 pages of supplementary informatio
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