A protein can fold into four different conformations. A) If the states are iso-e

Question

A protein can fold into four different conformations. A) If the states are iso-energetic, and the system has 1 mole of protein equally mixed between the four states, what is the entropy change of forcing it all into a single confirmation on a per mole basis? (This might occur for example during the process of crystallization.) B) Instead imagine that states B, C, D have a +1 kbT, +2 k,T, and +3 k,T energy increase compared to state A, respectively. What is the probability of finding the protein in each of the states? C) For the system in part (B), now what's the entropy change (on a per mole basis) of forcing the equilibrium mixture all to state A?

Explanation / Answer

a)the number of states

w = (3)^N0

where N0 = 6.02 x10^23

the entropy of equal population among the 3 states are

S = k ln w = N0k ln3

to force one state

w = 3 (any of one state )

S =kln3

deltaS = (N0-1)k ln3 ~ = N0kln3 = 8.31 *1.09 = 9.06 J/T

b) The probability in state A

1/(1+exp(-1)+exp(-2)

in State B is

exp(-1)/(1+exp(-1)+exp(-2)

in state C

exp(-2)/(1+exp(-1)+exp(-2)

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