The energy cost of polypeptide knot formation and its folding consequences

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.

Mechanical unfolding of a knotted protein unveils the kinetic and thermodynamic consequences of threading a polypeptide chain

“…In other words, the value of ∆∆G knot likely represents the energy cost paid by the unfolded state to form a knot just by chance. This value is similar to the knotting cost calculated for the artificial knotted protein Arc-L1-Arc 34 .…”

“…S2A), a value that is 7 nm shorter than the one expected for the full-length protein, Lc theoretical = 30.3 nm (84 residues between the pulling points). Similar differences of 4-6 nm have been reported in single molecule studies designed to tight a trefoil (3 1 ) knot in the unfolded state 24,[32][33][34] . It is important to highlight that MJ0366 is a homodimer in solution, and no information regarding monomer association or dimer dissociation steps can be extracted from our experiments due to the tethering constrains used to mechanically unfold MJ0366 ( Supplementary Fig.…”

Knotted proteins: Tie etiquette in structural biology

“…However, when non-native interactions are included, the knotting propensity raises considerably along the folding process. This behavior may result from the fact that non-native interactions energetically stabilize partially folded conformations, therefore lowering the free energy barrier of the entropically costly knotting step (85). Furthermore, for this protein, the knotting step also consists of a direct threading movement of the C-terminus, in line with that observed by Shakhnovich for YibK (56).…”

Developing the tube theory for polymer knots

“…Recently, knots in DNA [5][6][7][8][9][10] and proteins [11][12][13][14][15] have been observed in many experiments. Many intriguing or even counterintuitive phenomena have been found for polymer knots [16][17][18][19][20].…”