A protein molecule has two adjacent sites for ligand binding. The binding energy for a single ligand to either of the sites is εb. When both binding sites are occupied by ligands, the two ligands interact favourably with each other (this is called cooperativity) so the total binding energy is reduced by an amount εcoop. The concentration of ligand molecules in solution is c (in units of some standard concentration c0) and the energy of a ligand molecule in solution is εsol. What are the probabilities of finding the protein molecule with

(a) no ligand molecules bound?

(b) one ligand molecule bound?

(c) two ligand molecules bound?





where Δε = εb - εsol