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Chem288_2005_PS3 - Spring 2005 Problem Set 3 Handed out...

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Spring 2005 Problem Set 3 Chemistry 288 – Marohn Handed out: Friday, 11 February 2005 Due: Thursday, 17 February 2005 1. Double-stranded DNA melting. DNA exists as a twisted pair of polymer molecules, each with N monomer units. The two molecules are cross-linked by N base pairs. It requires an energy ε to unlink each base pair, and a base pair can be unlinked only if it has a neighboring base pair that is already unlinked (or if it is at the end of the molecule). Suppose that there are G orientations which each open link can assume: that is, the open state of a link is G -fold degenerate, corresponding to rotational freedom of the chain in the uncrosslinked state. (a) Find the probability that n pairs are unlinked at temperature T if one end of the molecule is prevented from unlinking, so the molecule “unwinds” from only end. (b) Calculate the average number ( n ) of pairs unlinked at a given temperature T . (c) Calculate the fraction f = ( n ) /N of DNA which is unlinked.
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