Mobility and Separation of Knotted Polymers

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)

Abstract

Knotting happens naturally in biological polymers, such as proteins and DNA, and plays a role in the basic mechanisms of cell functioning and replicating.

For this reason, recently there has been increasing interest in studying knots in long macromolecules and in understanding the role of topology in their behaviour.

One interesting problem is how to separate molecules according to their knot type, all the other characteristics being the same.

Inspired by the widely-used laboratory tool, agarose-gel electrophoresis, I present a minimal model of knotted macromolecular chains moving through a suspension and the results of simulations performed with my own code. I show that with a medium of small spheres at the vertices of a regular lattice, the topology has an effect on the rate of diffusion. Specifically, in the absence of a driving force more complex knots tend to move more slowly than simpler knots, while the opposite happens in the presence of a sufficiently strong field.

Additionally, I present a more biologically-oriented system, with longer molecules modelled after DNA, moving in a suspension of random spheres of comparable size to the radius of gyration of the chains, and I show the results of simulations performed with the molecular-dynamics program LAMMPS. I show that in the presence of a driving force and if the suspension spheres are in random motion, the rate of mobility increases linearly with the complexity of the knot.

Finally, I explore the possibility of phase separating a binary mixture of molecules according to their knot type. With the simulations performed so far, it has not been possible to show any evidence of phase separation, but the results can be used to establish limits on the parameters of the problem, and I have made some suggestions about possible future research in this area.
Date of Award29 Sep 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorSimon Hanna (Supervisor) & Annela M Seddon (Supervisor)

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