Effects of Side Chains on Polymer Knots
2019
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: Fbarrier/kBT ≈ 75Rg/Lknot, where kB is the Boltzmann
constant, T is the temperature, Rg is the radius of gyration of a side chain, and Lknot 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 polymersknotting and pore translocation.
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