Question Protein conformations Assume a prtein has six diffe

Question

Protein conformations: Assume a prtein has six different discrete conformations, with energies given:

A) -5 kcal mol^-1

B)-3 kcal mol^-1

C)-3 kcal mol^-1

D)1 kcal mol ^-1

E)1 kcal mol^-1

F)2 kcal mol ^-1

Questions:

1) Write an expression for the probability p(i) of finding the protein in conformation i.

2) Write an expression for the probability p(E) of finding the protein having energy E.

3) Use the expressions you wrote in (1) and (2) to calculate the following probabilities:

i)p(StateB)

ii)p(StateA)

iii)p(StateD)

iv)p(1 kcal mol^-1)

v)p(-5 kcal mol^-1)

4) What is the average energy of the ensemble of conformations?

The expression for the probability p(i) of finding the protein in conformation i. P(i) =1/6 where i = A, B, C, D, E, and F

2) The expression for the probability p(E) of finding the protein having energy E. p(-5 kcal mol^-1) = 1/6

p(-3 kcal mol^-1) =2/6 = 1/3 ;p(1 kcal mol^-1) =2/6 = 1/3 ; p(2 kcal mol^-1) =1/6

3) Use the expressions you wrote in (1) and (2) to calculate the following probabilities:

i)p(StateB) = p( state B) =1/6

ii)p(StateA) = 1/6

iii)p(StateD)= 1/6

iv)p(1 kcal mol^-1) =2/6 = 1/3

v)p(-5 kcal mol^-1)= 1/6

4) What is the average energy of the ensemble of conformations?

Average energy is = (-5*1/6) + (-3*1/3) + (1*1/3)+(2*1/6)=(-7/6) kcal mol^-1