A Circuit Topology Approach to Categorizing Changes in Biomolecular Structure

Frontiers in Physics

卷:8

Jaie Woodard¹  Arash Tirandaz²  Alireza Mashaghi²  Otto Schullian³ 

[1] Chemistry and Chemical Biology, Harvard University, Cambridge, MA, United States;

[2] Faculty of Mathematics and Natural Sciences, Leiden Academic Centre for Drug Research, Leiden University, Leiden, Netherlands;

[3] Max Planck Institute of Colloids and Interfaces, Department Theory and Biosystems, Potsdam, Germany;

[4] School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran;

关键词: topology;    matrix representation;    protein folding;    protein engineering;    permutation;    duplication;   

DOI  :  10.3389/fphy.2020.00005

来源: DOAJ

【 摘 要 】

The biological world is composed of folded linear molecules of bewildering topological complexity and diversity. The topology of folded biomolecules such as proteins and ribonucleic acids is often subject to change during biological processes. Despite intense research, we lack a solid mathematical framework that summarizes these operations in a principled manner. Circuit topology, which formalizes the arrangements of intramolecular contacts, serves as a general mathematical framework to analyze the topological characteristics of folded linear molecules. In this work, we translate familiar molecular operations in biology, such as duplication, permutation, and elimination of contacts, into the language of circuit topology. We show that for such operations there are corresponding matrix representations as well as basic rules that serve as a foundation for understanding these operations within the context of a coherent algebraic framework. We present several biological examples and provide a simple computational framework for creating and analyzing the circuit diagrams of proteins and nucleic acids. We expect our study and future developments in this direction to facilitate a deeper understanding of natural molecular processes and to provide guidance to engineers for generating complex polymeric materials.

【 授权许可】

Unknown