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Proteins are chains of amino acids linked together by peptide bonds. Upon synthesis, a protein folds into a three-dimensional conformation, critical to its biological function. Interactions between its constituent amino acids guide protein folding, and hence the protein structure is primarily dependent on its amino acid sequence.
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Updated: Jul 10, 2026

Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web

Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web

Published on: July 16, 2017

Curve encirclement and protein structure.

Patrick Kessler¹, Oliver M O'Reilly

¹Department of Mechanical Engineering, University of California, Berkeley, California 94720-1740, USA. watchwrk@me.berkeley.edu

Physical Review Letters

|November 13, 2007

Summary

This summary is machine-generated.

A new method quantifies how space curves encircle each other, distinguishing engaged and self-engaged curves. This technique is applied to analyze protein backbone chain topology.

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Area of Science:

Topology
Computational Biology
Biophysics

Background:

Understanding the spatial arrangement of molecular structures is crucial in biology.
Protein backbone chains exhibit complex three-dimensional conformations.
Quantifying topological entanglement in biological macromolecules remains a challenge.

Purpose of the Study:

To introduce a novel mathematical method for measuring curve encirclement.
To develop a quantitative approach for characterizing topological engagement in curves.
To apply this method to analyze the structural complexity of protein backbone chains.

Main Methods:

Development of a method based on a family of sets to characterize encircling curves.
Distinguishing between curve pairs that engage and single curves that self-engage.
Application of the method to the analysis of protein backbone chain topology.

Main Results:

The introduced method successfully measures the extent of curve encirclement.
The technique allows for the differentiation of engaged and self-engaged curve configurations.
Initial application demonstrates the utility of the method in analyzing protein structures.

Conclusions:

The developed method provides a robust tool for quantifying curve encirclement.
This approach offers new insights into the topological properties of molecular chains.
The findings have potential implications for understanding protein folding and function.