Consider a protein that has 100 amino-acids, where each amino-acid can have 3 possible orientations in the unfolded state. A single, unique, configuration of the chain corresponds to the native (folded) state. Assume that the entropic contribution to the free energy of the folded and unfolded states is entirely from the configurational entropy of the chain, and that the entropy and enthalpy are independent of temperature. (a) What is the entropy of the folded state? 4 (b) What is the entropy of the unfolded state? (c) The folding temperature Te for a protein is defined as the temperature at which half the molecules are in the folded state, and half are in the unfolded state. Let TF = 50C for this protein. At this temperature, what is difference in free energy between the folded and the unfolded states of the protein? (d) What is the difference in the enthalpy between the folded and the unfolded states of the protein? Recall that AG = AH - TAS, and assume that AH and AS are independent of temperature. (e) Write down an expression for the probability (Pn) that the protein is in the native (folded) state as a function of AG and the temperature T. (f) Plot Pn as a function of temperature, between 10 and 80 C. Verify that this probability is 1 at low temperature, 0 at high temperature, and 12 at the folding temperature TF