Question

Calculate the conformational entropy associated with the folding of a 75 amino acid peptide into a protein. Assume there are 3 conformational states for each side chain.

Compute the energy associated with the entropy change required to reach the folded state.

Estimate the energy associated with the hydrophobic collapse of this peptide to the folded state and compare the two. What does this say about the role of the hydrophobic effect in protein folding?

Revise your answer for a for the transition from unfolded peptide to molten globule. Assume that the molten globule has 1/2 the number of conformational states available to each amino acid. Does this change your answer for b?

Please use pictures to illustrate your thinking.

Answer 1

We have the relationship that:

∆G= ∆H- T∆S

Also, ∆Gfolding= 0

Therefore, -∆H= - T∆S

∆Hfolding= T∆Sfolding.

Now, S= RlnW

Here W= no. Of microstates

= No. Of conformation

Let's assume that each conformation state have equal energy.

Given, there are 3 conformation for each side chain.

Therefore, S= 8.314 ln3

= 9.1 J/K mol.

If T value is known, ∆Hfolding can be calculated.

For example, if T= 500°C= 773 K

∆Hfolding= 773× 9.1 J/mol.

=7060.4 J/mol

If only single side chain is used in folding.

So, the enthalpy of folding (∆Hfolding)= 7060.4 J/mol.

Now, given we have 75 amino acids and their are 3 conformation in each side chain.

So, totally we have = 75×3= 225 conformation and each is of same energy.

Now, no. Of microstates= 225

So, S= 8.314 ln225

=8.314× 5.416

= 45.029 J/K mol

Hence, ∆Hfolding= 773× 45.029 J/mol.

= 34807.7716 J/mol.

The hydrophobic effect is is the primary driving force for protein folding because
a folded protein is able to form the most hydrogen bonds.

The overall three-dimensional shape of an entire protein molecule is the tertiary structure. The protein molecule will bend and twist in such a way as to achieve maximum stability or lowest energy state. Although the 3-dimensional shape of a protein may seem irregular and random, it is fashioned by many stabilizing forces due to bonding interactions between the side-chain groups of the amino acids.