University of SaskatchewanHARVEST
  • Login
  • Submit Your Research
  • About
    • About HARVEST
    • Guidelines
    • Browse
      • All of HARVEST
      • Communities & Collections
      • By Issue Date
      • Authors
      • Titles
      • Subjects
      • This Collection
      • By Issue Date
      • Authors
      • Titles
      • Subjects
    • My Account
      • Login
      JavaScript is disabled for your browser. Some features of this site may not work without it.
      View Item 
      • HARVEST
      • Electronic Theses and Dissertations
      • Graduate Theses and Dissertations
      • View Item
      • HARVEST
      • Electronic Theses and Dissertations
      • Graduate Theses and Dissertations
      • View Item

      Strand Passage And Knotting Probabilities In An Interacting Self-Avoiding Polygon Model

      Thumbnail
      View/Open
      SCHMIRLER-THESIS.pdf (1.286Mb)
      Date
      2012-09-19
      Author
      Schmirler, Matthew
      Type
      Thesis
      Degree Level
      Masters
      Metadata
      Show full item record
      Abstract
      The work presented in this thesis develops a new model for local strand passage in a ring polymer in a dilute salt solution. This model, called the Interacting Local Strand Passage (ILSP) model, models ring polymers via Theta-SAPs, which are self-avoiding polygons (SAPs) in the simple cubic lattice that contain a fixed structure Theta. This fixed structure represents two segments of the self-avoiding polygon being brought ''close'' together for the purpose of performing a strand passage. Theta-SAPs were first studied in the Local Strand Passage (LSP) model developed by Szafron (2000, 2009), where each Theta-SAP is considered equally likely in order to model good solvent conditions. In the ILSP model, each Theta-SAP has a modified Yukawa potential energy which contains an attractive term as well as a screened Coulomb potential that accounts for the effect of salt in the model. The energy function used in this model was first proposed by Tesi et al. (1994) for studying self-avoiding polygons in the simple cubic lattice. The ILSP model is studied in this thesis using the Interacting Theta-BFACF (I-Theta-BFACF) Algorithm, an algorithm which is developed in this thesis and is proven to be ergodic on the set of all Theta-SAPs of a particular knot type and connection class. The I-Theta-BFACF algorithm was created by modifying the Theta-BFACF algorithm developed by Szafron (2000, 2009) to include energy-based Metropolis sampling. This modification allows one to sample Theta-SAPs of a particular knot type and connection class based on a priori chosen solvent conditions. Multiple simulations (each consisting of 40 billion time steps) of composite Markov Chain Monte Carlo implementations of the I-Theta-BFACF algorithm are performed on unknotted connection class II Theta-SAPs over a wide range of salt concentrations. The data from these simulations is used to estimate, as a function of polygon length, the probability of an unknotted Theta-SAP remaining an unknot after a strand passage, as well as the probability of it becoming a positive trefoil knot. The results strongly suggest that as the length of a Theta-SAP goes to infinity, the probability of the Theta-SAP becoming knotted after a strand passage increases as the salt concentration in the model increases. These results serve as a first step for studying how the knot reduction factor (studied by Liu et al. (2006) and Szafron and Soteros (2011)) of a ring polymer varies in differing solvent conditions. The goal of this future research is to find solvent conditions and a local geometry of the strand passage site that yields a knot reduction factor comparable to the research of Rybenkov et al. (1997), which shows an 80-fold reduction of knotting after type II topoisomerase enzymes act on DNA.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Soteros, Christine E.
      Committee
      Bickis, Miķelis G.; Szafron, Michael L.; Li, Longhai; Kusalik, Anthony J.
      Copyright Date
      September 2012
      URI
      http://hdl.handle.net/10388/ETD-2012-09-670
      Subject
      Mathematics
      Statistics
      Topoisomerase
      MCMC
      Markov Chain Monte Carlo
      Metropolis Sampling
      DNA
      Self Avoiding Polygons
      Collections
      • Graduate Theses and Dissertations
      University of Saskatchewan

      University Library

      © University of Saskatchewan
      Contact Us | Disclaimer | Privacy