Question

A 500 amino acid protein consists of 200 hydrophobic residues. Upon folding, 150 of the hydrophobic amino acids fold and form a hydrophobic core. Determine the ∆G o for the protein at 300K, considering contributions from both the protein and the water. Assume the following: When the protein folds, each amino acid (hydrophobic and hydrophilic) forms an interaction that is 3 kJ/mol more stable thant the unfolded state. In the unfolded state, the hydrophobic amino acids contact and influence the mobility of 2 water molecules. In the folded state, they do not contact either water. Water has 2 available conformations when it interacts with a hydrophobic sidechain. 6 conformations when it is free in solution.

Answer 1

Given data:

Chemical transformation:

Unfolded amino acids ([U]) < -------- > Folded amino acids([F])

Total number of amino acids = 500

Total hydrophobic residues = 200

No. of amino acids folded = 150

SO, No. of amino acids unfolded = 200-150 = 50

For above transformation,

Keq. = [F]/[U]= No. of folded a.a / No. of unfolded a.a.

Keq. = 150 / 50

Keq. = 3.

Now, standard Gibb’s free energy change (ΔG⁰) at any temperature T (K) is related with Keq. As,

(ΔG⁰) = -RTln(Keq.)…………………..(1)

We have, Keq. = 3, T = 300 K, R = 8.314 J.K^-1.mol^-1 , put all these values in eq.(1)

(ΔG⁰) = -8.314 x 300 x ln(3)……………….(Natural logarithm)

(ΔG⁰) = -8.314 x 300 x 1.099

(ΔG⁰) = -2741 J

(ΔG⁰) = -2.741 kJ……………..(since, 1J = 10^-3 kJ)

Hence standard Gibb’s free energy for protein folding is -2.741 kJ.

(ΔG⁰) = -ve

i.e. (ΔG⁰) < 0

I.e. reaction favors folded state.

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