Problem:

Zipper Model for DNA Unbinding Problem:

The unwinding of two-stranded DNA helix molecules can be described by a simplified zipper model: A zipper has N links; each link comes in two states, namely closed (energy 0) and open (energy \epsilon>0). We require that the zipper can unzip only from one side, say the left, and that in order for the link number s to unzip, all other links to its left (1, 2, . . . , s?1) must already be open as well.

Required:

Question 1: Show that the partition function Z(T, N) for this problem is Z(T,N) = [1-e^[-(N+1)\epsilon /kbT]] / [1-e^(-\epsilon/kbT)].

Question 2: Compute the average number of open links at fixed temperature T. Determine its behavior at low and high temperatures.

Show your calculations, but you do not need to write out any explanation.