Question $5.$ Shown below is a binding isotherm for ligand binding to a homodimeric protein

$(1)$ The protein has two binding sites for the ligand. What are the values of the $K_{DS}$ for each binding site? Show how you can graphically estimate the answer by sketching on the diagram.

$(2)$ Does the protein exhibit positive or negative cooperativity? Explain your answer.

$(3)$ What is the value of the Hill Coefficient for this system? Show how you can obtain the answer graphically, by sketching on the diagram. Show that this answer is consistent with the value of the Hill coefficient obtained by using a formula.