Sequence Determines Degree of Knottedness in a Coarse-Grained Protein Model

Knots are abundant in globular homopolymers but rare in globular proteins. To shed new light on this long-standing conundrum, we study the influence of sequence on the formation of knots in proteins under native conditions within the framework of the hydrophobic-polar (HP) lattice protein model. By employing large scale Wang-Landau simulations combined with suitable Monte Carlo trial moves we show that, even though knots are still abundant on average, sequence introduces large variability in the degree of self-entanglements. Moreover, we are able to design sequences which are either almost always or almost never knotted. Our findings serve as proof of concept that the introduction of just o…