Prediction of the optimal set of contacts to fold the smallest knotted protein

Knotted protein chains represent a new motif in protein folds. They have been linked to various diseases, and recent extensive analysis of the Protein Data Bank shows that they constitute 1.5% of all deposited protein structures. Despite thorough theoretical and experimental investigations, the role of knots in proteins still remains elusive. Nonetheless, it is believed that knots play an important role in mechanical and thermal stability of proteins. Here, we perform a comprehensive analysis of native, shadow-specific and non-native interactions which describe free energy landscape of the smallest knotted protein (PDB id 2efv). We show that the addition of shadow-specific contacts in the loop region greatly enhances folding kinetics, while the addition of shadow-specific contacts along the C-terminal region (H3 or H4) results in a new folding route with slower kinetics. By means of direct coupling analysis (DCA) we predict non-native contacts which also can accelerate kinetics. Next, we show that the length of the C-terminal knot tail is responsible for the shape of the free energy barrier, while the influence of the elongation of the N-terminus is not significant. Finally, we develop a concept of a minimal contact map sufficient for 2efv protein to fold and analyze properties of this protein using this map.