Consider two solution chambers of equal volume divided by a dialysis membrane that is impermeable to antibody molecules but permeable to small antigens. Starting with an antigen concentration of 4.8 nM in both chambers, you add its specific IgG antibody to one of the chambers at 1 nM concentration. You then measure the concentration of the antigen in the other chamber after equilibrium is reached, which turns out to be about 4 nM. What is the association constant (K_a) for the binding of the antigen to each antigen-binding site of IgG? Assume independent antigen-binding sites in each antibody molecule. Write down your answer in liters per mole, in scientific notation with one decimal place, e.g. 5.0 × 10² liters/mole).

Question

Quizplus · Accepted Answer

Free antigen concentration in both chambers is 4 nM at equilibrium, which means the concentration of bound antigen in the antibody-containing chamber is 1.6 nM, that is (4.8 nM - 4 nM) × 2, to account for the total antigen present in both chambers. This is also equal to the concentration of bound antigen-binding sites (not antibodies). Therefore, the concentration of unbound sites in this chamber is 0.4 nM, that is (1 nM × 2 - 1.6 nM). The association constant of antigen (Ag) binding to antigen-binding site (Abs) is thus calculated as:
K? = [Abs-Ag]?q/([Abs]?q[Ag]?q) = (1.6 nM)/(0.4 nM × 4 nM) = 1 liter/nmol = 1.0 × 10? liters/mole.

Consider Two Solution Chambers of Equal Volume Divided by a Dialysis