(468c) Relaxation of Knotted Polymers

In recent years, there has been interest in understanding the dynamics of knotted DNA due to the fact that such molecules have been observed in nanotechnology applications such as single-molecule gene-mapping and sequencing. In this talk, we will discuss our latest experiments and simulations to characterize the relaxation behavior of knotted chains from a highly extended initial state. The single-molecule experiments we perform repeatedly stretches and relaxes a knotted DNA in a microfluidic T-junction via an extensional electric field. We observe several findings: (1) the knots swell at a time scale that is comparable to the end-to-end relaxation of the polymer chain, and (2) the swelling behavior is fairly insensitive to the chain topology, at least for the large knots we sample. These results are corroborated by Brownian dynamic simulations, which are able to sample a wide range of knot topologies and several chain sizes. We note that in the experiments performed, the DNA contour length is much larger than the contour stored in a tight knot (75 microns to 2 microns). In the last part of the talk, we will discuss how knots alter the stress relaxation of shorter polymer chains. We perform Brownian dynamic simulations and develop scaling theories to understand how a finite-size knot at the center of the chain alters the polymer’s entropic elasticity and effective drag.