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).

1) Compute the difference in binding free energy (at a physiological temperature T=310 K) for the complexes. Provide the difference as a positive numerical expression with three significant figures in kJ/mol.

2) Divide the difference between the binding free energies of the ED₁ and ED₂ complexes by the thermal energy (at the physiological temperature). Provide a numerical expression with 3 significant figures.

3)

Compute the total concentration of [D₁]_tot that is needed to bind 90% 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.

4)

Compute the total concentration of [D₁]_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.

5)

Compute the total concentration of [D₂]_tot that is needed to bind 90% 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.

6)

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

1.Binding Free Energy is given by

where K_D is the dissociation constant.

Similary for D2

2. Thermal energy emitted by an average man(consuming 2500 calories) at 310k in 1 day = 10.5MJ

= 1.130*10^-3.

3.

Now suppose we want % of E bound to D1, i.e % of [E] = [ED1].

when = 90

[D1] = .9 * 10^-9 = .900 nM.

4. using the same formula

= 99

[D1] = .99 *10^-9 = .990nM

5. similarly for D2

K_D = 10^-7

= 90

[D2] = .9*10^-7 = .090

6. = 99

[D2] = .99*10^-7 = .099