Effects of knot type in the folding of topologically complex lattice proteins

The folding properties of a protein whose native structure contains a 5₂ knot are investigated by means of extensive Monte Carlo simulations of a simple lattice model and compared with those of a 3₁ knot. A 5₂ knot embedded in the native structure enhances the kinetic stability of the carrier lattice protein in a way that is clearly more pronounced than in the case of the 3₁ knot. However, this happens at the expense of a severe loss in folding efficiency, an observation that is consistent with the relative abundance of 3₁ and 5₂ knots in the Protein Data Bank. The folding mechanism of the 5₂ knot shares with that of the 3₁ knot the occurrence of a threading movement of the chain terminus that lays closer to the knotted core. However, co-concomitant knotting and folding in the 5₂ knot occurs with negligible probability, in sharp contrast to what is observed for the 3₁ knot. The study of several single point mutations highlights the importance in the folding of knotted proteins of the so-called structural mutations (i.e., energetic perturbations of native interactions between residues that are critical for knotting but not for folding). On the other hand, the present study predicts that mutations that perturb the folding transition state may significantly enhance the kinetic stability of knotted proteins provided they involve residues located within the knotted core.