A topological selection of folding pathways from native states of knotted proteins

TL;DR

This paper introduces a topologically inspired statistical method to analyze and classify knotted proteins, revealing different folding pathways and structural features through topology and geometry analysis validated by simulations.

Contribution

It presents a novel topological metric for comparing knotted protein structures, enabling the detection of folding pathway differences and structural clustering.

Findings

Identified geometric differences between trefoil proteins.

Revealed distinct folding pathways for shallow and deep knotted proteins.

Validated folding pathway differences with Molecular Dynamics simulations.

Abstract

Understanding the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geometry of knotted proteins by analysing the distribution of a protein's planar projections using topological objects called knotoids. We approach the analysis of proteins with the same topology by introducing a topologically inspired statistical metric between their knotoid distributions. We detect geometric differences between trefoil proteins by characterising their entanglement and we recover a clustering by sequence similarity. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for proteins forming open-ended trefoil knots. Interestingly, our pipeline reveals that the folding pathway of shallow knotted Carbonic Anhydrases involves the creation of a double-looped structure, differently from what was previously observed for deeply knotted trefoil proteins. We validate this with Molecular Dynamics simulations.