The thermal denaturation of the Peyrard–Bishop model with an external potential

Abstract

The impact of various types of external potentials on the Peyrard–Bishop DNA denaturation is investigated through the statistical mechanics approach. The partition function is obtained using the transfer integral method, and the stretching of hydrogen bonds is calculated using the time-independent perturbation method. It is shown that all types of external potentials accelerate the denaturation processes at lower temperature. In particular, it is argued that the Gaussian potential with infinitesimal width reproduces a constant force at one end of the DNA sequence as was already done in some previous works.

Helix untwisting and bubble formation in circular DNA

“…Somewhat different sets of parameters have be used in other studies to test the (homogeneous) anharmonic PB model albeit without rotational degrees of freedom [27][28][29][30]. Morse parameters and harmonic force constants have been recently obtained also for RNA, fitting the PB model to the experimental melting temperatures [31].…”

Mesoscopic model parametrization of hydrogen bonds and stacking interactions of RNA from melting temperatures

“…The model can also be used under a variety of theoretical frameworks such as path-integral formalism (16) or wavelet analysis (17), just to give a few examples. One attractive feature of the model is the ease by which one may modify the Hamiltonian to reflect certain properties of DNA such as the addition of solvation barriers (18,19), external forces (20) and other modified potentials (21). …”

The Viscous and External Forces Effect on the Thermal Denaturation of Peyrard-Bishop Model

“…The external factor is usually calculated by considering an additional term to the morse potential. For example, the external potential in the form of Gaussian will strengthen DNA separation process at low temperature [6]. In the Monte Carlo experiment the unzipping processes due to the external force probed show the dependence of the unzipping forces on unzipping speed and temperature [7].…”

“…It is possible that the local opening of DNA bubbles in the selective regions without breaking the whole DNA [5]. In other cases, the denaturation can also be influenced by many factor such as the alkaline compound filling up a cell, liquid surrounding DNA and other external potential [4][5][6][7][8]. It has been shown that a bell shaped soliton exists in the DNA chain when the effect of viscosity is taken into account [9,10].…”

“…Another hands, for the special case, if the external potential is treated as a small perturbation then the first order perturbation theory can be applied. This yields a smooth denaturation transition for homogeneous DNA [6]. If the external factor is considered, the path integral approach becomes the general case because the perturbative approximation is not used.…”