Mechanics of Twisted DNA Molecule Adsorbed on a Biological Membrane

DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. The study of DNA molecule achieved in vitro while submitting the DNA to all chemicals agent capabilities to destabilize links hydrogen, such as pH, temperature. In fact, the DNA enveloped in the membrane cellular, so it is legitimate to study the influence of membrane undulations. In this work, we try to show that the fluctuations of the membrane can be considerate as a physics agent is also capable to destabilize links hydrogen. In this investigation, we assume that each pair base formed an angle an with the membrane’s surface. We have proposed a theoretical model, and we have established a relationship between the angle formed by the pair base θeq and an angle formed by the membrane and each pair base. We assume that DNA and biomembrane interact via a realistic potential of Morse type. To this end, use is made of a generalized model that extends that introduced by M. Peyrard and A. R. Bishop in the past modified by M. Zoli. This generalized model is based on the resolution of a Schrodinger-like equation. The exact resolution gives the expression of the ground state, and the associated eigenvalue (energy) that equals the free energy, in the thermodynamic limit. First, we compute the denaturation temperature of DNA strands critical temperature. Second, we deduce all critical properties that mainly depend on the parameters of the model, and we quantify the effects of the membrane undulations. These undulations renormalize all physical quantities, such as harmonic stacking, melting temperature, eigenfunctions, eigenvalues and regular part of specific heat.