Th e denaturation of a biological macromolecule can be described by the equilibrium macromolecule in native form

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Question:

Th e denaturation of a biological macromolecule can be described by the equilibrium macromolecule in native form 7 macromolecule in denatured form:

a. Show that the fraction theta of denatured macromolecules is related to the equilibrium constant Kd for the denaturation process by theta= Kd / (1 + Kd)

b. Write an expression for the temperature dependence of Kd in terms of the standard enthalpy and standard entropy of denaturation

c. At pH = 2, the standard enthalpy and entropy of denaturation of the enzyme chymotrypsin are +418 kJ mol-1 and + 1.32 kJ kJ K-1 mol-1, respectively. Using these data and your results from parts (a) and (b), plot theta against T. Compare the shape of your plot with that of the plot with that of the plot shown in Fig. 3.16.

d. The ‘melting temperature’ of a biological macromolecule is the temperature at which theta = ½. Use your results from part (c) to calculate the melting temperature of chymotrypsin at pH = 2

e. Calculate the standard Gibbs energy and the equilibrium constant for the denaturation of chymotrypsin at pH = 2.0 and T = 310K (body temperature). Is the protein stable under these conditions?