80,244 research outputs found
Evolutionary distances in the twilight zone -- a rational kernel approach
Phylogenetic tree reconstruction is traditionally based on multiple sequence
alignments (MSAs) and heavily depends on the validity of this information
bottleneck. With increasing sequence divergence, the quality of MSAs decays
quickly. Alignment-free methods, on the other hand, are based on abstract
string comparisons and avoid potential alignment problems. However, in general
they are not biologically motivated and ignore our knowledge about the
evolution of sequences. Thus, it is still a major open question how to define
an evolutionary distance metric between divergent sequences that makes use of
indel information and known substitution models without the need for a multiple
alignment. Here we propose a new evolutionary distance metric to close this
gap. It uses finite-state transducers to create a biologically motivated
similarity score which models substitutions and indels, and does not depend on
a multiple sequence alignment. The sequence similarity score is defined in
analogy to pairwise alignments and additionally has the positive semi-definite
property. We describe its derivation and show in simulation studies and
real-world examples that it is more accurate in reconstructing phylogenies than
competing methods. The result is a new and accurate way of determining
evolutionary distances in and beyond the twilight zone of sequence alignments
that is suitable for large datasets.Comment: to appear in PLoS ON
Kinetic distance and kinetic maps from molecular dynamics simulation
Characterizing macromolecular kinetics from molecular dynamics (MD)
simulations requires a distance metric that can distinguish
slowly-interconverting states. Here we build upon diffusion map theory and
define a kinetic distance for irreducible Markov processes that quantifies how
slowly molecular conformations interconvert. The kinetic distance can be
computed given a model that approximates the eigenvalues and eigenvectors
(reaction coordinates) of the MD Markov operator. Here we employ the
time-lagged independent component analysis (TICA). The TICA components can be
scaled to provide a kinetic map in which the Euclidean distance corresponds to
the kinetic distance. As a result, the question of how many TICA dimensions
should be kept in a dimensionality reduction approach becomes obsolete, and one
parameter less needs to be specified in the kinetic model construction. We
demonstrate the approach using TICA and Markov state model (MSM) analyses for
illustrative models, protein conformation dynamics in bovine pancreatic trypsin
inhibitor and protein-inhibitor association in trypsin and benzamidine
A methodology for determining amino-acid substitution matrices from set covers
We introduce a new methodology for the determination of amino-acid
substitution matrices for use in the alignment of proteins. The new methodology
is based on a pre-existing set cover on the set of residues and on the
undirected graph that describes residue exchangeability given the set cover.
For fixed functional forms indicating how to obtain edge weights from the set
cover and, after that, substitution-matrix elements from weighted distances on
the graph, the resulting substitution matrix can be checked for performance
against some known set of reference alignments and for given gap costs. Finding
the appropriate functional forms and gap costs can then be formulated as an
optimization problem that seeks to maximize the performance of the substitution
matrix on the reference alignment set. We give computational results on the
BAliBASE suite using a genetic algorithm for optimization. Our results indicate
that it is possible to obtain substitution matrices whose performance is either
comparable to or surpasses that of several others, depending on the particular
scenario under consideration
Robust computation of linear models by convex relaxation
Consider a dataset of vector-valued observations that consists of noisy
inliers, which are explained well by a low-dimensional subspace, along with
some number of outliers. This work describes a convex optimization problem,
called REAPER, that can reliably fit a low-dimensional model to this type of
data. This approach parameterizes linear subspaces using orthogonal projectors,
and it uses a relaxation of the set of orthogonal projectors to reach the
convex formulation. The paper provides an efficient algorithm for solving the
REAPER problem, and it documents numerical experiments which confirm that
REAPER can dependably find linear structure in synthetic and natural data. In
addition, when the inliers lie near a low-dimensional subspace, there is a
rigorous theory that describes when REAPER can approximate this subspace.Comment: Formerly titled "Robust computation of linear models, or How to find
a needle in a haystack
Regularized Wasserstein Means for Aligning Distributional Data
We propose to align distributional data from the perspective of Wasserstein
means. We raise the problem of regularizing Wasserstein means and propose
several terms tailored to tackle different problems. Our formulation is based
on the variational transportation to distribute a sparse discrete measure into
the target domain. The resulting sparse representation well captures the
desired property of the domain while reducing the mapping cost. We demonstrate
the scalability and robustness of our method with examples in domain
adaptation, point set registration, and skeleton layout
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