2. DNA subjected to a stretching force exceeding 60 pN undergoes a structural tr

Question

2. DNA subjected to a stretching force exceeding 60 pN undergoes a structural transition from the usual B form to the so-called S form (S for stretch). Here we examine a simple model of this transition based on the freely jointed chain model of DNA. Consider the freely jointed chain model in one dimension. Each link of the polymer points in the +x- or the -x-direction. There is a force fin the +x-direction applied at one of the ends (see the following figure). To account for the B-to-S transition, we assume that links are of length b (B state) or a (S state), with a > b Furthermore, there is an energy penalty e of transforming the link from a B state to an S state. (This is the energy, presumably, for unstacking the base pairs.) (Hint, Each link of the polymer can have four states: it can have length a or b and it can point in either the or the - direction.) (20 points) (a) Write down the expressions for the total energy for each of the four states of a single link (5 points). (b) Write down the expressions for the Boltzmann factor for each of the four states of a single link (5 points). (c) Write down the expressions for the partition function of a single link (5 points)

Explanation / Answer

b) It takes energy to point far from the direction of the force; so every energy of + direction have a (length • F) term. Polymer's each link can have four states: it can have length a or b and it can point in either the + or – direction. It takes energy to point away from the direction of the force; so all the + direction energies have a –(length*F) term.

d)

The average end-to-end distance L of a single link is

beFb+ae(Fa)beFbae(+Fa)

¿L>¿statesLP(L)=1/z¿

And the average length of N links is D = N<L>

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