The transfer integral operator method in the study of DNA unzipping and bubble formation

In this work we reexamine the unzipping and bubble formation of DNA in the context of the PeyrardBishopDauxois DNA model using the transfer integral operator method. After a brief overview of the method, we use it to calculate the probabilities that consecutive base-pairs are stretched beyond a threshold amplitude. We compare the continuous PeyrardBishopDauxois model with an Ising-type model and demonstrate their similarities. For the PeyrardBishopDauxois model, we derive an expression for the force that is required to open a double-stranded sequence at one end while the other end is kept closed. In the thermodynamic limit, we use this expression to study the dependence of the unzipping force on the temperature. We also calculate the opening probabilities in the case of zero force and in the case where a force is applied in the middle of the sequence. Analytically, the case where the force is applied in the middle is similar to the case of a homogeneous DNA sequence of strong GC pairs with a defect, in the form of a weaker AT base pair, in the middle. Numerical results verify this similarity.