An RNA oligonucleotide has the sequence A6C7U6. It can form a hairpin loop held together b...

An RNA oligonucleotide has the sequence A6C7U6. It can form a hairpin loop held together by a maximum of six A • U base pairs:

Assume that the helical region can melt only from either end. Use the notation s = equilibrium constant for adding a base pair to a helical region and σj ws = equilibrium constant for initiating the first base pair forming a loop. The subscript j = 7,9, 11, 13, 15, 17 characterizes the number of unpaired bases in the loop.

a. Calculate the statistical weight of each species that can be present.

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b. Calculate the mole fraction of each species that can be present.

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c. Assume that the molar absorptivity of each species depends on only the number of base pairs formed: ε0 = absorptivity per mole of mononucleotide for species with no base pairs, ε1 = absorptivity of all species with one base pair, etc. Write an expression for the absorbance in a 1-cm cell of a solution of A6C7U6 in terms of s, σj, εj and c = concentration of A6C7U6 in moles of nucleotides per liter