Consider a protein with four equivalent and independent binding sites for a ligand.

A$)$ Find the intrinsic dissociation constant, Kd$,$ given fractional saturation point of the enzyme with four substrates is $67\mathrm{.}00\%$ at a ligand concentration of $0\mathrm{.}005$ millimolar.

B$)$ What is the standard Gibbs energy change of ligand dissociation for this protein at $298\mathrm{.}0$ K$?($Hint: Be sure to express the dissociation constant in units that are consistent with the standard state.$)$

C$)$ Draw a Scatchard plot for this enzyme. Then draw two new curves on the plot. One should represent what happens when the number of binding sites is decreased to three. The other should represent what happens when the affinity for the ligand is increased. Your plot should have three curves, labeled axes, and possibly other descriptive marks.

D$)$ Sketch a plot for the fractional saturation of sites as a function of ligand concentration for the three different scenarios presented in part $($C$)$ of this problem. $($i$.$e$.$ four binding sites, three binding sites with the same Kd$,$ and four binding sites with an increased affinity for the ligand.$)$ You may do this for either the ligand concentration or the logarithm of the ligand concentration, but you must indicate which you are using. Your plot should contain three curves, labeled axes, the location of the Kd values, and the location of the maximal fractional saturation values.

Give a thorough a thorogh and detailed answer