Knotting in Flexible-Semiflexible Block Copolymers

Recent experiments observed that knots occur in polymers, including DNA and proteins, and affect rheological and biological properties. Inspired by these observations, researchers are motivated to find effective ways to control knot properties. In this work, using Monte Carlo simulations, we find the nonuniform bending stiffness in flexible-semiflexible block copolymers can effectively control the probability, size, position, and shape of knots. First, the knotting probability dramatically increases with the block length, L_block. Second, the knot size, which is defined as the contour length of the knot core, prefers to be L_knot = 2nL_block (n = 1, 2, 3, ···). Third, knots strongly prefer to locate at the sites such that the knot boundaries stay at semiflexible blocks. The occurrences of knots at the preferred site can be 30 times more frequent than the unpreferred site. Such preference is caused by the dramatic variation of bending within a knot core, i.e., some regions of the knot core have sharp bending, while some regions have little bending. Lastly, the knots at preferred sites have distinct shape features. Our results deepen the understanding of the roles of bending in knot formation and can be used to effectively control knot properties by modulating the nonuniform bending stiffness along a polymer.