Topology, Geometry, and Stability: Protein Folding and Evolution

TL;DR

This paper explores how topological features influence protein folding and evolution, emphasizing the importance of scale-invariant properties in understanding protein stability and shape formation.

Contribution

It introduces a topological approach to analyze protein folding stability and proposes a connection between topological features and biological evolution.

Findings

Topological features are potentially central to protein stability.

Shape and folding are linked to sequence via topology.

Implications for understanding protein evolution.

Abstract

The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows that features without length scales, i.e. topological features, are potentially of central importance. Topology is a natural mathematical tool for the study of shape and we avail ourselves of that tool to examine the relationship between the amino acid sequence and the shapes of protein molecules. We apply what we learn to conjectures about their biological evolution.