Knots and Swelling in Protein Folding

TL;DR

This paper investigates the rarity of knotted proteins, proposing that knots cause swelling in short proteins, and uses simulations to predict optimal sizes for different knots, linking structure to biological scarcity.

Contribution

It introduces a hypothesis that knots cause swelling in short proteins and provides simulation-based predictions of optimal protein sizes for specific knots.

Findings

Knots tend to cause swelling in proteins shorter than 200 amino acids.

Monte Carlo simulations show the figure-8 knot is most compact in 200-600 amino acids.

Theoretical upper bounds for trefoil knot size align with PDB data.

Abstract

Proteins can sometimes be knotted, and for many reasons the study of knotted proteins is rapidly becoming very important. For example, it has been proposed that a knot increases the stability of a protein. Knots may also alter enzymatic activities and enhance binding. Moreover, knotted proteins may even have some substantial biomedical significance in relation to illnesses such as Parkinson's disease. But to a large extent the biological role of knots remains a conundrum. In particular, there is no explanation why knotted proteins are so scarce. Here we argue that knots are relatively rare because they tend to cause swelling in proteins that are too short, and presently short proteins are over-represented in the Protein Data Bank (PDB). Using Monte Carlo simulations we predict that the figure-8 knot leads to the most compact protein configuration when the number of amino acids is in the range of 200-600. For the existence of the simplest knot, the trefoil, we estimate a theoretical upper bound of 300-400 amino acids, in line with the available PDB data.