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Unformatted text preview: 1 PS#5 20.110/2.772 Fall 2008 2.772/20.110 Problem Set #5 Due Friday October 17 in 16429 at 3pm NO LATE PSETS WILL BE ACCEPTED Please submit the problems as: 2, 4 3,5, 7 6 ,9, 10 1, 8 1.) ELVIS is everywhere a.) Given 20 naturally occurring amino acids, what is the probability that the amino acid sequence ELVIS occurs in a stretch of a protein sequence? b.) What is the probability if the order of the amino acids did not matter, i.e., VLSEI, etc.? 2.) Levinthal’s Paradox: Cyrus Levinthal, a former MIT professor, claimed that proteins can not go from unfolded to folded state by sampling of all possible states. He claimed that it would take way too long for a protein to fold if they were to sample all possible conformations (proteins fold on the order of ~ms to ~ μ s). Assume that a protein has 100 amino acids and each amino acid has two degrees of freedom (angles of rotation called φ and ψ ), also assume that it takes a femtosecond to sample each conformation. Using simple statistics show that Prof. Levinthal was indeed right and that it would take a very long time (much longer than our lifetimes!) if the protein was to sample all possible conformations. If proteins were to fold by sampling all possible states, calculate the change in entropy upon folding, assume that the unfolded state has all the possible states and the folded state is unique (i.e there is only one folded state). (Hint : Use Boltzmann’s definition of entropy). 3.) The statistical thermodynamics of a cooperative system. (Dill and Bromberg) Perhaps the simplest statistical mechanical system having ‘cooperativity ’is the threelevel system in the following table....
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 Fall '08
 GRIFFITH
 DNA, molar entropy, average energy

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