Wavelet coefficients as a guide to DNA phase transitions.

Abstract

Physical statistics models such as the Peyrard-Bishop model are extensively used to study thermodynamic properties of DNA. One of the interesting aspects of this model is that it is a one-dimensional model exhibiting phase transitions which can be continuously changed from smooth to very sharp transitions. The partition function for the Peyrard-Bishop model can be calculated using the transfer integral technique yielding an eigenfunction which can be interpreted as a probability density. In this work we show that it is possible to expand the eigenfunction of the transfer integral operator using methods commonly used in wavelet signal analysis. The wavelet coefficients obtained from multiresolution analysis can be used as a tool to monitor the melting transition. This method is numerically very efficient and addresses the issue of eigenfunction localisation which can be employed in problems that make use of the transfer integral technique, demonstrating the application of wavelet multiresolution analysis in phase transition.