Only need to answer problem 3, and problem 2 for refer.

Problem 3. [10 pts.] Refer to Problem 2 in this assignment set. For simplicity, set =1. Assume that the hydrogen bonding energy () between the oxygen atom in monomer j and the hydrogen in monomer j+4 is temperature-independent and is equal to 2.5kBTroom. A reasonable choice of the multiplicity of a monomer in a coil state is WC=9. What is then the melting temperature (in units of Troom )? Problem 2. [10 pts.] (a) Refer to the matrix formalism approach to the coil-helix transition in a homogeneous polypeptide chain. Obtain Z3 (total sum of weights) and compare it with what we obtained in class. Express the fractional helicity in terms of relevant quantities such as s (weight for a H after another H ) and s (weight for a H after a C). (b) Why is the coil-helix transition sharper for smaller ? Explain why. Problem 3. [10 pts.] Refer to Problem 2 in this assignment set. For simplicity, set =1. Assume that the hydrogen bonding energy () between the oxygen atom in monomer j and the hydrogen in monomer j+4 is temperature-independent and is equal to 2.5kBTroom. A reasonable choice of the multiplicity of a monomer in a coil state is WC=9. What is then the melting temperature (in units of Troom )? Problem 2. [10 pts.] (a) Refer to the matrix formalism approach to the coil-helix transition in a homogeneous polypeptide chain. Obtain Z3 (total sum of weights) and compare it with what we obtained in class. Express the fractional helicity in terms of relevant quantities such as s (weight for a H after another H ) and s (weight for a H after a C). (b) Why is the coil-helix transition sharper for smaller ? Explain why