Coloring Invariant for Topological Circuits in Folded Linear Chains

Symmetry, vol. 13, pp. 919

Abstract

Circuit topology is a mathematical approach that categorizes the arrangement of contacts within a folded linear chain, such as a protein molecule or the genome. Theses linear biomolecular chains often fold into complex 3D architectures with critical entanglements and local or global structural symmetries stabilised by formation of intrachain contacts. Here, we adapt and apply the algebraic structure of quandles to classify and distinguish chain topologies within the framework of circuit topology. We systematically study the basic circuit topology motifs and define quandle/bondle coloring for them. Next, we explore the implications of circuit topology operations that enable building complex topologies from basic motifs for the quandle coloring approach.

Authors 3

1. Jose Ceniceros

   Hamilton College

   Affiliation as printed

   Mathematics and Statistics Department, Hamilton College, Clinton, NY 13323, USA

2. Mohamed Elhamdadi

   University of South Florida

   Affiliation as printed

   Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

3. Alireza Mashaghi corresponding Aachen Medical Systems Biophysics and Bioengineering Leiden Academic Centre for Drug Research Faculty of Science, Leiden University

   Leiden University

   Affiliation as printed

   Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, 2333 CC Leiden, The Netherlands