The peptide Special-K forms an a-helix that is broken at high temperatures. The fraction of peptide in the a-helical form (fraction = moles a-helical peptide/total moles of peptide), aH, was measured over a range of temperatures:
T(K) 324.4 326.1 327.5 329.0 330.7 332.0 333.8
aH 0.961 0.893 0.787 0.595 0.345 0.167 0.045
a) Calculate the equilibrium constant, K, and molar Gibbs free energy, deltaG, for helix formation at 54.3°C (assume a 1M solution).
b) Special-K contains one histidine residue. Calculate the fraction of Special-K molecules in which the histidine is positively charged at 25°C and pH 6.5.
His-H2+ <-> His-(H+) + H+ pKa1 = 1.8 deltaH = 0
His-H+ <-> His + H+ pKa2 = 6.0 deltaH = 30 kJ/mol
His <-> His- + H+ pKa3 = 9.2 deltaH = 44 kJ/mol
c) As the temperature of the peptide is increased, the Ka of the histidine residue will change. Based on this, will the fraction of charged histidine residues increase or decrease (you don’t need to calculate a value, but show reasoning) as the temperature is raised from 25°C to 54.4°C at pH 7?