Why do polymers knot and proteins (k)not?
Thomas Wüst (Swiss Federal Research Institute WSL)

It is a long-standing conundrum why only few knots are observed in proteins while they are abundant in globular homopolymers. Biologically and evolutionary motivated hypotheses and explanations have been proposed but they are hardly quantifiable. In this project we follow a statistical physics approach and investigate the influence of the additional degree of freedom from hydrophobic (H) and polar (P) residues in coarse-grained lattice HP proteins on the formation of self-entanglements and knots. With a very powerful Monte Carlo sampling scheme it has been possible to reliably simulate HP protein chains up to 500 monomers. Our extensive simulations revealed that the thermodynamic average knottedness between homo- and heteropolymers is similar within this model. However, it is possible to design HP sequences featuring almost no knots (knot probability < 0.05) to full knottedness (knot probability > 0.85). This provides a "proof of concept" that a single degree of freedom (H/P) suffices that Nature (evolution) can naturally select sequences which do not form knots.