Biophysics: Protein converts into amyloid fibril by overcoming the free energy b

Question

Biophysics:

Protein converts into amyloid fibril by overcoming the free energy barrier of Delta G=20 kcal/mol. The mutation stabilizes protein native state by 2 kcal/mol. What will be the change in the rate of amyloid formation caused by the mutation? Assume that Arrhenius law k_{a}=k_{0}exp(-Delta G/RT) is applicable, where k_{a} is the rate of amyloid formation, Delta G is the free energy barrier separating native protein from amyloid state, and R is the gas constant. The temperature is T=300K, and the prefactor k_{0} is not affected by the mutation.

Explanation / Answer

Before the mutation

Delta G=20 kcal/mole, T=300K, R= 1.985 8775 × 10-3kcal /Kmol

k_{a}=k_{0}exp(-Delta G/RT)= k_{0} exp( -20/ (1.985 8775 × 10-3 *300))= k_{0}*2.63371*10-15 units.

After the mutation

Delta G=22 kcal/mole, T=300K, R= 1.985 8775 × 10-3kcal /Kmol

k_{a}=k_{0}exp(-Delta G/RT)= k_{0} exp( -22/ (1.985 8775 × 10-3 *300))= k_{0}*9.1754*10-17 units.

Change in rate of amyloid formation= k_{0}*2.63371*10-15- k_{0}*9.1754*10-17= k_{0}* 2.54196*10-15 units.

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