• 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. 

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.

𝓁p-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.

References

SHOWING 1-10 OF 32 REFERENCES

A topological measurement of protein compressibility

In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a

RCSB Protein Data Bank: powerful new tools for exploring 3D structures of biological macromolecules for basic and applied research and education in fundamental biology, biomedicine, biotechnology, bioengineering and energy sciences

New features and resources of the RCSB PDB have been described in detail using examples that showcase recently released structures of SARS-CoV-2 proteins and host cell proteins relevant to understanding and addressing the COVID-19 global pandemic.

Protein-Folding Analysis Using Features Obtained by Persistent Homology

GISA: using Gauss Integrals to identify rare conformations in protein structures

GISA, a general method which transforms a structure into a “fingerprint of topological-geometric values” consisting in a series of real-valued descriptors from mathematical Knot Theory, is proposed, allowing fingerprinting on any scale from local to global.

Elementary Applied Topology

Multidimensional scaling: I. Theory and method

Multidimensional scaling can be considered as involving three basic steps. In the first step, a scale of comparative distances between all pairs of stimuli is obtained. This scale is analogous to the

Evaluating protein structure descriptors and tuning Gauss integral based descriptors

This paper addresses the question of what should be required from a good set of protein structure descriptors and examines a Gauss integral based family of proteinructure descriptors, that has been shown to successfully classify the geometry of CATH2.4 connected protein domains.

CATH: expanding the horizons of structure-based functional annotations for genome sequences

An update of the latest data and developments within the CATH protein structure classification database, which adds layers of derived data, such as predicted sequence domains, functional annotations and functional clustering, to CATH+, the most recent CATH+ release.

Structures and mechanisms of glycosyl hydrolases.