Extended Topological Persistence and Contact Arrangements in Folded Linear Molecules

Frontiers in Applied Mathematics and Statistics

VerovÅ¡ek, Sara KaliÅ¡nik¹  Mashaghi, Alireza² 

[1]Department of Mathematics, Stanford University, Stanford, CA, USA

[2]Department of Ophthalmology, Harvard Medical School, Harvard University, Boston, MA, USA

关键词: Persistent homology;    Extended persistence;    Computational topology;    Biomolecular structure;    Circuit topology;    folding;   

DOI  :  10.3389/fams.2016.00006

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

Structure plays a pivotal role in determining the functional properties of self-interacting linear biomolecular chains, for example proteins and nucleic acids. In this paper, we propose a method for representing each such molecule combinatorially - as a one-dimensional simplicial complex - in a novel way that takes into account intra-chain contacts. The representation allows for efficient quantification of structural similarities and differences between molecules, and for studying molecular topology using extended persistence. This method performs a multi-scale analysis on a filtered simplicial complex as it tracks clusters, holes, and higher dimensional voids in the filtration. From extended persistence we extract information about the arrangement of intra-chain interactions, a topological property which demonstrably affects folding and unfolding dynamics of the linear chains.

【 授权许可】

CC BY