DNA Breathing Dynamics: Stochastic Modelling and Applications of Large Deviation Theory

Abstract

DNA breathing is a physiological phenomenon characterised by base pair bubbles within the DNA, which fluctuate in size due to thermal fluctuations. When DNA is heated it cooperatively unravels from a double-stranded DNA (ordered phase) to two single-stranded DNAs (disordered phase). This is called DNA melting and has been established as a first-order phase transition. The DNA is modelled as inspired by the Poland-Scheraga model and research by Altan-Bonnet and Co. focusing on homogeneous DNA and the single-bubble approach. This thesis investigates the stochastic approach to DNA breathing successfully showcasing the reliability of the Gillespie Algorithm in generating single trajectories for this process so it can be analysed on a microscopic scale following previous research. Furthermore, the possibility of a metastable state in DNA, characterised by the coexistence of the ordered and disordered phases is explored by applying Large Deviation Theory to the stochastic DNA model. The analysis indicates the potential for such a case however a diverging timescale remains crucial in confirming this hypothesis.