Please see the attached file:
Note only the energies associated with the unzipping have to be considered in the partition function; any energies from the bending, stretching, etc. of the molecule can be ignored.
A toy model for DNA molecules. A DNA molecule is made of two complementary strands, which are hold together by hydrogen bonds. A very simple model of a DNA molecule is that of a zipper which has N links; each link has a state in which it is closed with energy 0 and a state in which it is open with energy e. We require that the zipper only unzip from one side( say from the left) and the link can only open if all the links to the left of it (1, 2, ..., n-1) are already open.
a. find the partition function
b. find the average number of open links <n> and show that for low temperature kT<<e, <n> is independent of N.
The solution shows detailed calculation of finding the partition function and average number of open links of the zipper model for a DNA molecule.