(WTHS 3.16) Consider a monomeric protein, P, that can bind to two different ligands, A and B. The binding sites for the two ligands overlap, such that the second ligand cannot bind to a protein molecule already complexed with the first ligand, and vice versa.

a) Derive an expression for the equilibrium fraction of protein complexed with the first ligand when both ligands are present. How does the presence of the second ligand affect protein complexation with A? What happens to the fraction bound when the KD,B is very high?

b) You have an experimental setup in which the PA complex generates a signal, but the PB complex does not. You decide to estimate the KD,A by finding the ligand concentration of A at which the signal is half of the value approached using extremely high ligand concentrations. After collecting the data, you realize that your sample of ligand A was contaminated with ligand B. The initial contamination ratio is b = [B]/[A]. You can assume there is a high concentration of A compared to B. Please derive an expression for [A]50% signal in terms of KD,A, KD,B, and b. Will you calculate an affinity for A that is stronger or weaker than the true A affinity?