$[R]+[L]lar{r}_{k_2}{k}_{1}RL$

a$)$ Write a system of differential equations that governs the change in concentration of each

species $($R$,$ L$,$ and RL$)$ with respect to time $($i$.$e$.$ d$[$R$]/$dt$,$ etc$).$

b$)$ Assuming the total number of receptors is constant with time, a mass balance on the receptors

indicates that they are either free or bound at any point in time. Thus, $[R_{\text{T}\text{O}\text{T}}]=[R]+[RL].$

Similarly, a mass balance on the ligand yields: $[L_0]=[L]+[RL].$ Use this information to express

$d\frac{RL}{d}t$ in terms of constants and $[$RL$].$