H-bond simulation in DNA using a harmonic oscillator isospectral potential

In recent years several new potentials obtained from the supersymmetric formalism have been applied to quantum mechanics @1,2#. These potentials were derived from shape invariant potentials, and their mathematical and formal aspects have been discussed @3#. However, they have not been applied to any real physical system. In this work, we propose a problem where a harmonic oscillator isospectral potential obtained from superalgebra can be applied. The problem is the thermic denaturation of the DNA macromolecules, whose stability depends on the H bonds between the complementary base pairs as well as on the stacking interactions between adjacent bases along the strands. To achieve this goal, two ribbons of DNA are simulated by springs and masses linked together by anharmonic springs. Integral transfer operator formalism @4# is used to study this system. The applicability and free parameters of the proposed potential will be discussed in the context of thermal denaturation of the poly (A-T)-poly(A-T) DNA. The melting temperature of the poly(A)-poly(T) DNA can be reproduced by a change of the stacking interactions parameter.