• Corpus ID: 231925079

Persistent topology of protein space

@inproceedings{Hamilton2021PersistentTO,
  title={Persistent topology of protein space},
  author={W L Hamilton and Jacqueline E. Borgert and Thomas Hamelryck and J. S. Marron},
  year={2021}
}
Protein fold classification is a classic problem in structural biology and bioinformatics. We approach this problem using persistent homology. In particular, we use alpha shape filtrations to compare a topological representation of the data with a different representation that makes use of knot-theoretic ideas. We use the statistical method of Angle-based Joint and Individual Variation Explained (AJIVE) to understand similarities and differences between these representations.ย 
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4 Citations

A Topological Data Analysis Study on Murine Pulmonary Arterial Trees with Pulmonary Hypertension

This study uses novel methods from topological data analysis (TDA), employing persistent homology to quantify arterial network morphometry for control and hypertensive mice and shows that the pruning methods effects the spatial tree statistics and complexities of the trees.

Homology of homologous knotted proteins

A mathematical pipeline is developed that systematically analyzes protein structures and identifies important geometric features of protein entanglement and clusters the space of trefoil proteins according to their depth, which demonstrates the potential of this approach in contexts where standard knot theoretic tools fail.

๐“p-Distances on Multiparameter Persistence Modules

It is shown that on 1or 2-parameter persistence modules over prime fields, dp I is the universal metric satisfying a natural stability property; this result extends a stability result of Skraba and Turner for the p-Wasserstein distance on barcodes in the 1- parameter case, and is also a close analogue of a universality property for the interleaving distance given by the second author.

$\ell^p$-Distances on Multiparameter Persistence Modules

It is shown that on 1or 2-parameter persistence modules over prime fields, dp I is the universal metric satisfying a natural stability property; this result extends a stability result of Skraba and Turner for the p-Wasserstein distance on barcodes in the 1- parameter case, and is also a close analogue of a universality property for the interleaving distance given by the second author.

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