Consider the dimerization 2 A ⇌ A₂, with forward rate constant k_a and backward rate constant k_b.

(a) Derive the following expression for the relaxation time in terms of the total concentration of protein, [A]_tot, = [A] + 2[A₂]:

(b) Describe the computational procedures that lead to the determination of the rate constants k_a and k_b from measurements of τ for different values of [A]_tot.

(c) Use the data provided below and the procedure you outlined in part (b) to calculate the rate constants k_a and k_b, and the equilibrium constant K for formation of hydrogen-bonded dimers of 2-pyridone:

1 =k + 8kkb[A] tot