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Modeling DNA Replication Using the sine-Gordon Equation

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abstract
DNA replication begins when locally unzipped regions of several broken hydrogen bonds form which cause a partial unwinding of the double helix. These regions are often referred to as bubbles and their formation can be modeled using a chain of coupled pendula. The angular oscillations that occur are usually modeled using the sine-Gordon equation. In this model, the discrete analog of the sine-Gordon equation is derived. Instead of taking the continuous limit, the space step between pendula remains nonzero and the forces on each pendulum are considered. Additionally, the randomization of nitrogen bases, Adenine, Thymine, Guanine, and Cytosine, within the chain of pendula, is modeled by randomly selecting the corresponding coefficients for each base. The system of differential equations is solved and plotted using Verlet integration in MATLAB.
subject
coupled pendulums
DNA replication
sine-Gordon
contributor
Rogowski, Susan (author)
Raynor, Sarah (committee chair)
Moore, Frank (committee member)
Gemmer, John (committee member)
date
2019-05-24T08:35:44Z (accessioned)
2019-05-24T08:35:44Z (available)
2019 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/93954 (uri)
language
en (iso)
publisher
Wake Forest University
title
Modeling DNA Replication Using the sine-Gordon Equation
type
Thesis

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