LO $4\mathrm{.}2+4\mathrm{.}4-$Q$1$ Instead of looking at the kinetics of a drug interacting with an enzyme, you can use an assay such as a filter binding assay to measure the equilibrium dynamics of the interaction. In the assay results below, you used a constant concentration of a radio$-$labeled HIV drug Darunavir $(1$pM$)$ and added an increasing amount of HIV$-$Protease $($enzyme$)$ to your reaction. The results of the experiment are below.

Using the graph:

a$.$ Estimate the $\backslash ($ K$\_\{$d$\}\backslash )$ for Darunivir. $($Note that the radioactivity when the maximum amount of protein, $\backslash (50\backslash$mu $\backslash$mathrm$\{$M$\}\backslash ),$ was added the radioactive signal on the filter paper was $\backslash (1*10^\{6\}\backslash )$ counts$).$ b$.$ Calculate the $\backslash (\backslash$Delta G$\_\{\backslash$text $\{$bind $\}\}^\{$o$\}\backslash )$ for the interaction between HIV protease and Darunivir at $310$ K K

$\backslash ($ y $\backslash )$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

G$-$R T $\backslash$ln $($K R$)\backslash \backslash$

$0\backslash \backslash$

$0$

$\backslash$end$\{$array$\}$

$\backslash ]$

Binding of a drug to a protein is entropically unfavorable $(2$ molecules bind to form $1$ molecule$).$

Yestertion is VERY favorable. What are two ways that Darunivir$-$binding could overcome the large entropic unfavourability of binding for a net favorable reaction. Be specific.

Entropic Increase in Binding of the solvent that carraes it

Enthalpic increase in Binding $-$

The enthalpic encmease cap cone due to string H$-$bonds cleate cavoialde enthal pac rracractions

d$.$ Sketch a Hill Plot of the Darunivir binding to HIV Protease Data. Indicate what the slope, Xintercept, and Y$-$intercept would be$.$