3–13 An antibody binds to another protein with an equilibrium constant, K, of 5 × 109 M–1. When it binds to a second, related protein, it forms three fewer hydrogen bonds, reducing its binding affinity by 11.9 kJ/mole. What is the K for its binding to the second protein? (Free-energy change is related to the equilibrium constant by the equation ΔG° = –2.3 RT log K, where R is 8.3 × 10–3 kJ/(mole K) and T is 310 K.) 3–14 The protein SmpB binds to a special species of tRNA, tmRNA, to eliminate the incomplete proteins made from truncated mRNAs in bacteria. If the binding of SmpB to tmRNA is plotted as fraction tmRNA bound versus SmpB concentration, one obtains a symmetrical S-shaped curve as shown in Figure Q3–3. This curve is a visual display of a very useful relationship between Kd and concentration, which has broad applicability. The general expression for fraction of ligand bound is derived from the equation for Kd(Kd = [Pr][L]/[Pr–L]) by substituting ([L]TOT – [L]) for [Pr–L] and rearranging. Because the total concentration of ligand ([L]TOT) is equal to the free ligand ([L]) plus bound ligand ([Pr–L]), 1.0
Figure Q3–3 Fraction of tmRNA bound versus SmpB concentration (Problem 3–14).
concentration of SmpB (M)
For SmpB and tmRNA, the fraction bound = [SmpB– tmRNA]/[tmRNA]TOT = [SmpB]/([SmpB] + Kd). Using this relationship, calculate the fraction of tmRNA bound for SmpB concentrations equal to 104 Kd, 103 Kd, 102 Kd, 101 Kd, Kd, 10–1 Kd, 10–2 Kd, 10–3 Kd, and 10–4 Kd.
3–15 Many enzymes obey simple Michaelis–Menten kinetics, which are summarized by the equation where Vmax = maximum velocity, [S] = concentration of substrate, and Km = the Michaelis constant.
It is instructive to plug a few values of [S] into the equation to see how rate is affected. What are the rates for [S] equal to zero, equal to Km, and equal to infinite concentration?
3–16 The enzyme hexokinase adds a phosphate to D-glucose but ignores its mirror image, L-glucose. Suppose that you were able to synthesize hexokinase entirely from D-amino acids, which are the mirror image of the normal L-amino acids.
a.
Assuming that the “D” enzyme would fold to a stable conformation, what relationship would you expect it to bear to the normal “L” enzyme?
b.
Do you suppose the “D” enzyme would add a phosphate to L-glucose, and ignore D-glucose?
3–17 How do you suppose that a molecule of hemoglobin is able to bind oxygen efficiently in the lungs, and yet release it efficiently in the tissues?
3–18 Synthesis of the purine nucleotides AMP and GMP proceeds by a branched pathway starting with ribose 5-phosphate (R5P), as shown schematically in Figure Q3–4. Using the principles of feedback inhibition, propose a regulatory strategy for this pathway that ensures an adequate supply of both AMP and GMP and minimizes the buildup of the intermediates (A–I) when supplies of AMP and GMP are adequate.
0 0.25 0.5 0.75
Figure Q3–4 Schematic diagram of the metabolic pathway for synthesis of AMP and GMP from R5P (Problem 3–18).
Berg JM, Tymoczko JL & Stryer L (2011) Biochemistry, 7th ed. New York: WH Freeman.