Effects of Side Chains on Polymer Knots

As an intriguing phenomenon, knotting in DNA, proteins, and other molecules has been extensively investigated in recent years, not only because of fundamental interest in knotting but also because of significant effects of knotting on mechanical, rheological, chemical, and biological properties. Some polymers contain side chains, and the effects of side chains on polymer knots are not clear. In this work, we investigate the effects of side chains on knots through Langevin dynamics simulations of knot diffusion along a stretched polymer with side chains. When the gap between side chains is larger than the knot size; each side chain acts as a barrier to slow down the knot diffusion. We find that how a knot crosses the barrier by a side chain resembles how a polymer translocates a pore. Inspired by the latter, we find a simple empirical expression for the free energy barrier caused by a side chain: F_barrier/k_BT ≈ 75R_g/L_knot, where k_B is the Boltzmann constant, T is the temperature, R_g is the radius of gyration of a side chain, and L_knot is the contour length of the knot core. The equations and numerical results obtained in this work can guide the rational control of knot diffusivity along a polymer by side chains. In addition, our results provide insights into the understanding of knots in peptides and single-stranded DNA where side chains are common. Furthermore, this work makes a connection between two interesting phenomena for polymers - knotting and pore translocation.