You have engineered an IgG antibody with two equivalent sites that reversibly bind a monomeric soluble cytokine. Binding at one site does not impact the energetics of binding at the other site. What concentration of the cytokine maximizes the amount of singly bound antibody? Derive the answer in terms of total antibody concentration and the monovalent affinity K

Hint: The calculate the maximum you can derivative of the singly-bound fraction with respect to the ligand and set it to zero.