Analysing DNA structural parameters using a mesoscopic model

The Peyrard-Bishop model is a mesoscopic approximation to model DNA and RNA molecules. Several variants of this model exists, from 3D Hamiltonians, including torsional angles, to simpler 2D versions. Currently, we are able to parametrize the 2D variants of the model which allows us to extract important information about the molecule. For example, with this technique we were able recently to obtain the hydrogen bonds of RNA from melting temperatures, which previously were obtainable only from NMR measurements. Here, we take the 3D torsional Hamiltonian and set the angles to zero. Curiously, in doing this we do not recover the traditional 2D Hamiltonians. Instead, we obtain a different 2D Hamiltonian which now includes a base pair step distance, commonly known as rise. A detailed knowledge of the rise distance is important as it determines the overall length of the DNA molecule. This 2D Hamiltonian provides us with the exciting prospect of obtaining DNA structural parameters from melting temperatures. Our results of the rise distance at low salt concentration are in good qualitative agreement with those from several published x-ray measurements. We also found an important dependence of the rise distance with salt concentration. In contrast to our previous calculations, the elastic constants now show little dependence with salt concentrations which appears to be closer to what is seen experimentally in DNA flexibility experiments.