Suppose a protein can exist in two conformations that have an energy difference of 2.0 kJ/mol....
Suppose a protein can exist in two conformations that have an energy difference of 2.0 kJ/mol. What is the estimated ratio of the conformations at 25 C? Which conformation is more abundant and by what factor? SHOW WORK!
Homework Answers
Let the protein exist in two conformations 1 and 2 which exist in equilibrium as
Conformation 1 <======> Conformation 2
The equilibrium constant for the equilibrium is given as
K = [Conformation 2]/[Conformation 1]
The energy difference between the two conformations is 2.0 kJ/mol at 25ºC, i.e, ΔG0 = 2.0 kJ/mol at T = (25 + 273) K = 298 K.
We know that
ΔG0 = -RT*ln K
Plug in values and get
2.0 kJ/mol = -(8.314 J/mol.K)*(298 K)*ln K
====> (2.0 kJ/mol)*(1000 J)/(1 kJ) = -(8.314 J/mol.K)*(298 K)*ln K
====> 2000 J/mol = -(2477.572 J/mol)*ln K
====> ln K = (2000 J/mol)/(-2477.572 J/mol)
====> ln K = -0.80724
====> K = exp(-0.80724)
====> K = 0.44608 ≈ 0.45 (ans, correct to 2 sig. figs).
Therefore, the ratio of the two conformers at equilibrium is 0.45.
Since the ratio is less than 1, offcourse, conformation 1 is present in larger proportion as compared to conformation 2. It also turns out that conformation 1 is the more preferred conformation at equilibrium.
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