The energy cost of polypeptide knot formation and its folding consequences

Andrés Bustamante,Carlos Bustamante,Daniel G Guerra,Juan Sotelo-Campos,Martin Floor,Mauricio Báez,Christian A M Wilson

doi:10.1038/s41467-017-01691-1

Abstract

Knots are natural topologies of chains. Yet, little is known about spontaneous knot formation in a polypeptide chain—an event that can potentially impair its folding—and about the effect of a knot on the stability and folding kinetics of a protein. Here we used optical tweezers to show that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 120 residues is 5.8 ± 1 kcal mol−1. Monte Carlo dynamics of random chains predict this value, indicating that the free energy cost of knot formation is of entropic origin. This cost is predicted to remain above 3 kcal mol−1 for denatured proteins as large as 900 residues. Therefore, we conclude that naturally knotted proteins cannot attain their knot randomly in the unfolded state but must pay the cost of knotting through contacts along their folding landscape.

Highlights

We found that Arc-L1-Arc presents a 31 knot and populates an unknotted configuration in its native state
The free energy cost to form a trefoil knot in the denatured state of Arc-L1-Arc is high (5.8 ± 1 kcal mol−1) and independent of the protein sequence since this value is well predicted by Monte Carlo simulations of random chains[5, 6]
We took advantage of this feature to compare the energy associated with the unfolding of a knotted and unknotted protein and to determine the energetic cost to form a knot in the unfolded state

Summary

Introduction

Monte Carlo dynamics of random chains predict this value, indicating that the free energy cost of knot formation is of entropic origin This cost is predicted to remain above 3 kcal mol−1 for denatured proteins as large as 900 residues. The structural complexity and the presence of multiple intermediates prevented them from determining the effect of a knot on the thermodynamic stability of a protein and the cost of its spontaneous formation in the mechanically unfolded state[13]. The free energy cost to form a trefoil knot in the denatured state of Arc-L1-Arc is high (5.8 ± 1 kcal mol−1) and independent of the protein sequence since this value is well predicted by Monte Carlo simulations of random chains[5, 6]. We conclude that knots are avoided by their high cost of formation in unfolded chains and we surmise that naturally knotted proteins must have evolved specific folding pathways to pay the cost of knotting through contacts along their folding landscape

Methods

Results

Conclusion