| An n-string tangle is a three dimensional ball with n-strings properly embedded in it. In late the 1980's, C. Ernst and D. W. Sumner's introduced a tangle model for protein-DNA complexes. This model assumes that the protein is a 3-dimensional ball and the protein-bound DNA are strings embedded inside the ball.;Originally the tangle model was applied to proteins such as Cre recombinase which binds two DNA segments. This protein breaks and rejoins DNA segments and can create knotted DNA. We can use a 2-string tangle model for this complex. More recently, Pathania, Jayaram and Harshey predicted that the topological structure within aMu protein complex consists of three DNA segments containing five crossings. Since Mu binds DNA sequences at 3 sites, this Mu protein-DNA complex can be modeled by a 3-string tangle. Darcy, Leucke and Vazquez analyzed Pathania et al's experimental results by using 3-string tangle analysis.;Based on the 3-string tangle analysis of a Mu protein-DNA complex, we addressed the possibility that a protein binds DNA sequences at four sites. Such a protein complex bound to a circular DNA molecule is modeled by a 4-string tangle with four loops outside of the tangle. In this thesis, we determined a biologically relevant 4-string tangle model. We also developed mathematics for solving tangle equations to predict the topology of DNA within the protein complex. |
