The unzipping transition under the influence of external force of a dsDNA molecule has been studied using the Peyrard-Bishop Hamiltonian. The critical force F(c)(T) for unzipping calculated in the constant force ensemble is found to depend on the potential parameter k which measures the stiffness associated with a single strand of DNA and on D, the well depth of the on-site potential representing the strength of hydrogen bonds in a base pair. The dependence on temperature of F(c)(T) is found to be (T(D) - T)(1/2) (T(D) being the thermal denaturation temperature) with F(c)(T(D)) = 0 and F(c)(0) = [Formula: see text]. We used the constant extension ensemble to calculate the average force F(y) required to stretch a base pair a y distance apart. The value of F(y) needed to stretch a base pair located far away from the ends of a dsDNA molecule is found twice the value of the force needed to stretch a base pair located at one of the ends to the same distance for y >/= 1.0 A. The force F(y) in both cases is found to have a very large value for y approximately 0.2 A compared to the critical force found from the constant force ensemble to which F(y) approaches for large values of y. It is shown that the value of F(y) at the peak depends on the value of krho which measures the energy barrier associated with the reduction in DNA strand rigidity as one passes from dsDNA to ssDNA and on the value of the depth of the on-site potential. The effect of defects on the position and height of the peak in the F(y) curve is investigated by replacing some of the base pairs including the one being stretched by defect base pairs. The formation and behaviour of a loop of Y shape when one of the ends base pair is stretched and a bubble of ssDNA with the shape of "an eye" when a base pair far from ends is stretched are investigated.

We study the role of cations on the stability of double stranded DNA (dsDNA) molecules.It is known that the two strands of double stranded DNA(dsDNA) have negative charge due to phosphate group. Cations in the form of salt in the solution, act as shielding agents thereby reducing the repulsion between these strands. We study several heterogeneous DNA molecules. We calculate the phase diagrams for DNA molecules in thermal as well as in force ensembles using Peyrard-Bishop-Dauxois (PBD) model. The dissociation and the stacking energies are the two most important factors that play an important role in the DNA stability. With suitable modifications in the model parameters we investigate the role of cation concentration on the stability of different heterogeneous DNA molecules. The objective of this work is to understand how these cations modify the strength of different pairs or bases along the strand. The phase diagram for the force ensemble case (a dsDNA is pulled from an end) is compared with the experimental results

The cations, in form of salt, present in the solution containing DNA play a crucial role in the opening of two strands of DNA. We use a simple non linear model and investigate the role of these cations on the mechanical unzipping of DNA. The Hamiltonian is modified to incoporate the solvent effect and the cations present in the solution. We calculate the melting temperature as well as the critical force that is required to unzip the DNA molecule as a function of salt concentration of the solution. The phase diagrams are found to be in close agreement with the experimental phase diagrams

The effect of defects on the melting profile of short heterogeneous DNA chains are calculated using the Peyrard-Bishop Hamiltonian. The on-site potential on a defect site is represented by a potential which has only the short-range repulsion and the flat part without well of the Morse potential.The stacking energy between the two neigbouring pairs involving a defect site is also modified. The results are found to be in good agreement with the experiments.

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