Single-molecule experiments and simulations of knotted polymer chains


Vivek Narsimhan and Alex Klotz


Vivek Narsimhan, Alex Klotz, C. Benjamin Renner, Patrick S. Doyle

Author Affiliation: 

Dept of Chemical Engineering, Massachusetts Institute of Technology


Knots are found everywhere in our daily lives, whether they be fashion accessories or items to fasten two objects together. However, unknown to many people, knots also play an important role in biology. For example, knots alter the kinetics of DNA transcription, so much so that nature has evolved specific enzymes to control the topology of these chains. Driven by these observations, there has been considerable interest in recent years to understand how these self-entanglements alter the physical properties of polymers at the molecular scale. Here, we perform single-molecule experiments and Brownian dynamics simulations to understand how knots move along a polymer chain and how these entities alter the polymer's global dynamics. A few topics are highlighted below: A. Knots dramatically delay the onset of the coil-stretch transition of a polymer chain. B. Knots convect off a polymer chain under external flow. However, if applied tension is sufficiently large, the knots jam instead. We determine the conditions under which jamming occurs and determine what factors give rise to the internal friction in the knotted core. C. Knots reduce the relaxation time of a polymer strand. This effect arises because knots swell during relaxation and hence hasten the contraction of the polymer strand. D. Knots can halt the motion of polymers through nanopores by jamming at the pore entrance. However, if one cycles the external field on and off at a time scale comparable to the relaxation time of the knot, one can control the swelling of the knot at the pore entrance and hence design strategies to ratchet the polymer through the pore.