26,611 research outputs found
Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
This work introduces a number of algebraic topology approaches, such as
multicomponent persistent homology, multi-level persistent homology and
electrostatic persistence for the representation, characterization, and
description of small molecules and biomolecular complexes. Multicomponent
persistent homology retains critical chemical and biological information during
the topological simplification of biomolecular geometric complexity.
Multi-level persistent homology enables a tailored topological description of
inter- and/or intra-molecular interactions of interest. Electrostatic
persistence incorporates partial charge information into topological
invariants. These topological methods are paired with Wasserstein distance to
characterize similarities between molecules and are further integrated with a
variety of machine learning algorithms, including k-nearest neighbors, ensemble
of trees, and deep convolutional neural networks, to manifest their descriptive
and predictive powers for chemical and biological problems. Extensive numerical
experiments involving more than 4,000 protein-ligand complexes from the PDBBind
database and near 100,000 ligands and decoys in the DUD database are performed
to test respectively the scoring power and the virtual screening power of the
proposed topological approaches. It is demonstrated that the present approaches
outperform the modern machine learning based methods in protein-ligand binding
affinity predictions and ligand-decoy discrimination
Global Network Alignment
Motivation: High-throughput methods for detecting molecular interactions have lead to a plethora of biological network data with much more yet to come, stimulating the development of techniques for biological network alignment. Analogous to sequence alignment, efficient and reliable network alignment methods will improve our understanding of biological systems. Network alignment is computationally hard. Hence, devising efficient network alignment heuristics is currently one of the foremost challenges in computational biology. 

Results: We present a superior heuristic network alignment algorithm, called Matching-based GRAph ALigner (M-GRAAL), which can process and integrate any number and type of similarity measures between network nodes (e.g., proteins), including, but not limited to, any topological network similarity measure, sequence similarity, functional similarity, and structural similarity. This is efficient in resolving ties in similarity measures and in finding a combination of similarity measures yielding the largest biologically sound alignments. When used to align protein-protein interaction (PPI) networks of various species, M-GRAAL exposes the largest known functional and contiguous regions of network similarity. Hence, we use M-GRAAL’s alignments to predict functions of un-annotated proteins in yeast, human, and bacteria _C. jejuni_ and _E. coli_. Furthermore, using M-GRAAL to compare PPI networks of different herpes viruses, we reconstruct their phylogenetic relationship and our phylogenetic tree is the same as sequenced-based one
TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions
Although deep learning approaches have had tremendous success in image, video
and audio processing, computer vision, and speech recognition, their
applications to three-dimensional (3D) biomolecular structural data sets have
been hindered by the entangled geometric complexity and biological complexity.
We introduce topology, i.e., element specific persistent homology (ESPH), to
untangle geometric complexity and biological complexity. ESPH represents 3D
complex geometry by one-dimensional (1D) topological invariants and retains
crucial biological information via a multichannel image representation. It is
able to reveal hidden structure-function relationships in biomolecules. We
further integrate ESPH and convolutional neural networks to construct a
multichannel topological neural network (TopologyNet) for the predictions of
protein-ligand binding affinities and protein stability changes upon mutation.
To overcome the limitations to deep learning arising from small and noisy
training sets, we present a multitask topological convolutional neural network
(MT-TCNN). We demonstrate that the present TopologyNet architectures outperform
other state-of-the-art methods in the predictions of protein-ligand binding
affinities, globular protein mutation impacts, and membrane protein mutation
impacts.Comment: 20 pages, 8 figures, 5 table
Quantitative toxicity prediction using topology based multi-task deep neural networks
The understanding of toxicity is of paramount importance to human health and
environmental protection. Quantitative toxicity analysis has become a new
standard in the field. This work introduces element specific persistent
homology (ESPH), an algebraic topology approach, for quantitative toxicity
prediction. ESPH retains crucial chemical information during the topological
abstraction of geometric complexity and provides a representation of small
molecules that cannot be obtained by any other method. To investigate the
representability and predictive power of ESPH for small molecules, ancillary
descriptors have also been developed based on physical models. Topological and
physical descriptors are paired with advanced machine learning algorithms, such
as deep neural network (DNN), random forest (RF) and gradient boosting decision
tree (GBDT), to facilitate their applications to quantitative toxicity
predictions. A topology based multi-task strategy is proposed to take the
advantage of the availability of large data sets while dealing with small data
sets. Four benchmark toxicity data sets that involve quantitative measurements
are used to validate the proposed approaches. Extensive numerical studies
indicate that the proposed topological learning methods are able to outperform
the state-of-the-art methods in the literature for quantitative toxicity
analysis. Our online server for computing element-specific topological
descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/Comment: arXiv admin note: substantial text overlap with arXiv:1703.1095
Inference of Ancestral Recombination Graphs through Topological Data Analysis
The recent explosion of genomic data has underscored the need for
interpretable and comprehensive analyses that can capture complex phylogenetic
relationships within and across species. Recombination, reassortment and
horizontal gene transfer constitute examples of pervasive biological phenomena
that cannot be captured by tree-like representations. Starting from hundreds of
genomes, we are interested in the reconstruction of potential evolutionary
histories leading to the observed data. Ancestral recombination graphs
represent potential histories that explicitly accommodate recombination and
mutation events across orthologous genomes. However, they are computationally
costly to reconstruct, usually being infeasible for more than few tens of
genomes. Recently, Topological Data Analysis (TDA) methods have been proposed
as robust and scalable methods that can capture the genetic scale and frequency
of recombination. We build upon previous TDA developments for detecting and
quantifying recombination, and present a novel framework that can be applied to
hundreds of genomes and can be interpreted in terms of minimal histories of
mutation and recombination events, quantifying the scales and identifying the
genomic locations of recombinations. We implement this framework in a software
package, called TARGet, and apply it to several examples, including small
migration between different populations, human recombination, and horizontal
evolution in finches inhabiting the Gal\'apagos Islands.Comment: 33 pages, 12 figures. The accompanying software, instructions and
example files used in the manuscript can be obtained from
https://github.com/RabadanLab/TARGe
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