Tightness of knots in a polymer chain.

It was predicted recently that sufficiently complex knots on a linear wormlike chain can have a metastable size, preventing their spontaneous expansion. We tested this prediction via computer simulations for 7(1) and 10(151) knots. We calculated the equilibrium distributions of knot size S for both knots. By using the umbrella sampling, we were able to obtain the distributions over a wide range of S values. The distributions were converted into the dependencies of the free energy on the knot size. The obtained free energy profiles have no pronounced local minima, so there are no metastable knot sizes for these knots. We also performed Brownian dynamics simulation of 7(1) knot relaxation that started from a very tight knot conformation. The simulation showed that knot expansion is a fast process compared to knot displacement along the chain contour by diffusion.