Question

Similar to the lecture, our example is a drug molecule D and a drug target enzyme E. The drug target enzyme E is commonly found in concentrations [E]_tot of 250 nM, i.e. 2.5 x 10^-7 mol/l. The drug D binds to E to form the complex ED with a dissociation constant of KD = 1.30 µM (i.e. 1.30 x 10^-6). The dissociation constant has been determined at room temperature, i.e. for T = 298.15 K.

1. In order to estimate the effectivity of the drug D, calculate the ratio of the concentration of the free, unbound drug molecules [D] and the bound complex [ED], i.e. [D]/[ED], for the conditions described in part B. Provide your answer with 3 significant figures.

2. Long hours of work in the lab have reveled an improved version of the drug, D', which forms an additional hydrogen bond with the drug target enzyme E. This results in an overall stabilization of the complex ED' relative to ED and the binding free energy for ED' is 10.5 kJ/mol more negative than for ED. What is the resulting dissociation constant for the complex ED' at room temperature? Provide your answer in units of mol/l and with 3 significant figures.

3. Which total concentration of the drug D', [D']_tot, is needed to bind 50% of the drug target enzyme E into the complex ED'? Provide your answer in units of mol/l and with 3 significant figures.

4. In order to estimate the effectivity of the drug D', calculate the ratio of the concentration of the free, unbound drug molecules [D'] and the bound complex [ED'], i.e. [D']/[ED']. Provide your answer with 3 significant figures.

Answer 1

1. we have,

   E + D <==> ED

Kd = 1/k = [E] [D] / [ED] = 1.30 x 10^-6 M

[D] / [ED] = Kd/[E]

we take [E] ~ [ED]

thus, [D] / [ED] = 1.30 x 10^-6 M / 2.5 x 10^-7 M

[D] / [ED] = 5.20

2.   An overall stabilization of the complex ED' relative to ED and the binding free energy for ED' is 10.5 kJ/mol more negative than for ED.

We assume E--D follows transition state theory :

Being other thing similar except transition state energy and stabilization of ED complex :

total stabilization : 10.5 kJ/mol

Kd(D) / Kd(D') = e^{−(ΔG )/RT} /  e^{−(ΔG-10.5 kJ/mol)/RT}

=  exp (( -10.5 kJ/mol)/RT)

= exp (( -10500 J/mol) /8.314 J/K-mol* 298.15K)

Kd(D) / Kd(D') = 0.0145

Kd(D') = 8.99*10^-5 M

3.   Which total concentration of the drug D', [D']_tot, is needed to bind 50% of the drug target enzyme E into the complex ED'? Provide your answer in units of mol/l and with 3 significant figures.

we have, fraction of enazyme that are bound by drug:

0.5 = [D'] / [D']+Kd'

0.5 { [D']+Kd' } = [D'] = 8.99*10^-5 M

or Kd' = [D']