Spring 2005Problem Set 3Chemistry 288 – MarohnHanded out: Friday, 11 February 2005Due: Thursday, 17 February 20051.Double-stranded DNA melting.DNA exists as a twisted pair of polymer molecules, each withNmonomerunits. The two molecules are cross-linked byNbase pairs. It requires an energyεto 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 theend of the molecule). Suppose that there areGorientations which each open link can assume: that is, the openstate of a link isG-fold degenerate, corresponding to rotational freedom of the chain in the uncrosslinked state.(a) Find the probability thatnpairs are unlinked at temperatureTif one end of the molecule is preventedfrom unlinking, so the molecule “unwinds” from only end.(b) Calculate the average number(n)of pairs unlinked at a given temperatureT.(c) Calculate the fractionf=(n)/Nof DNA which is unlinked.
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