Document Type


Date of Degree

Summer 2013

Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Darcy, Isabel

First Committee Member

Ayati, Bruce

Second Committee Member

Mitchell, Colleen

Third Committee Member

Stroyan, Keith

Fourth Committee Member

Washington, Todd


For many years scientists have been working on more advanced methods to determine the structure of DNA under various conditions. However, research on the study of the shape of DNA segments bound by protein (protein-bound DNA) has been limited by the accuracy and dependability of laboratory techniques. These techniques vary from gel electrophoresis experiments, which can determine the topological shape of unbound DNA, to experiments that crystallize protein-bound DNA in a fixed state in order to determine the spatial location of non-hydrogen atoms. Each method comes with its own benefits and drawbacks. One drawback is experiments used to determine the exact geometry for protein-bound DNA often fail for large complexes. So when laboratory techniques fail to yield a geometric description of the DNA bound by protein, we turn to modeling software.

We introduce software that takes known protein-bound DNA topology and determines a potential geometry. An n-string tangle consists of n strings embedded in a three-dimensional ball with endpoints fixed on the boundary. The strings represent the DNA segments bound by protein. Starting with a topological tangle file from KnotPlot (a knot and tangle visualization program), our software minimizes over geometric parameters while keeping the topology fixed.

Our modeling software assumes the base pairs to be rigid bodies (or rectangles). Our routine minimizes over an energy function established by Dr. Wilma Olson et al. for the software package, 3DNA. Our program differs from 3DNA in that it can determine potential geometric structures while remaining consistent with the known topology. Thus, for protein-bound DNA whose topology has been identified, we can associate a likely geometry.

The energy function over which we minimize is given in terms of dimer geometric parameters derived from crystal structures of protein-bound DNA. A dimer refers to two consecutive DNA base pairs. Thus, not only is our solution topologically relevant, but the geometric solution is DNA sequence specific. Currently only two-dimensional models for protein-bound DNA tangles are easily available. Thus, one of the main benefits of our software is that it offers three-dimensional visualization of the protein-bound DNA segments. This modeling software is a great starting point for determining potential geometries for protein-bound DNA, analyzing the geometrical shape of the bound DNA, and learning more about how the topology and geometry of protein-bound DNA structures are associated.


Applied Mathematics, Biology, Geometry, Protein-bound DNA, Software, Topology


xii, 147 pages


Includes bibliographical references (pages 141-147).


Copyright 2013 Mary Therese Padberg