Question

As discussed during the lecture, the enzyme HIV-1 reverse transcriptae (HIV-RT) plays a significant role for the HIV virus and is an important drug target. Assume a concentration [E] of 2.00 µM (i.e. 2.00 x 10^-6 mol/l) for HIV-RT. Two potential drug molecules, D₁ and D₂, were identified, which form stable complexes with the HIV-RT.

The dissociation constant of the complex ED₁ formed by HIV-RT and the drug D₁ is 1.00 nM (i.e. 1.00 x 10^-9 mol/l). The dissociation constant of the complex ED₂ formed by HIV-RT and the drug D₂ is 100 nM (i.e. 1.00 x 10^-7 mol/l).

Compute the total concentration of [D₂]_tot that is needed to bind 99% of the HIV-RT at the given concentration [E]_tot. Provide your answer as a numerical expression with 3 significant figures in the unit mol/l.

You do NOT have to consider competition betwwen the drugs D₁ and D₂! They are administered separately.

Answer 1

We have the drug D2 binding HIV-RT (enzyme E) to form the complex ED2:

                                                                                             

The dissociation constant is given by:

                                                                                              

where [E]_u is the concentration of unbound enzyme and [D2]_u is the concentration of unbound D2 at equilibrium.

The fraction of [E] that is bound by [D2] =

                                                               

where [E]_tot is the total concentration of E.

Now,

                                                                    

Similarly,

                                                                 

where [D2]_tot is the total concentration of D2.

So,                   

i.e.                                                                

Given, fraction of bound [E] = 99% = 0.99

                                                         

So,

Given K_d = 1 x 10^-7mol/l for E and D2

So,

Hence, for a total concentration of D2 of 1.18 x 10^-5mol/l, 99% of the given concentration of HIV-RT will be bound to D2.