Question

6) Proteins are composed of amino acids polymerized into long chains. The structure of a protein - that is, its overall shape and how the chains are "folded” around each other - is very important for its function. In an aqueous environment, in an active, folded state the hydrophilic amino acids in the protein are facing outwards exposed to the water and the hydrophobic amino acids are hidden away from the water in the core of the protein. In a general way we can conceptualize an equilibrium between the folded structure and the inactive, unfolded structure of a protein simply as: unfolded folded a) for this general reaction, would you expect the values of AH and AS to be positive, negative, or zero? Explain your answer. 5 pts) b) Imagine a situation where you have taken a position in a biology lab studying protein structures. Your colleagues have recently isolated a novel new protein from jellyfish that is fluorescent when in its folded structure. You find upon heating up the protein that it stops fluorescing when unfolded. This fact allows you to run some fluorescence spectroscopy experiments to easily study the equilibrium of the folded and unfolded protein at various temperatures. After conducting these experiments, you find that at 5 °C (which happens to be the average temperature of the sea water in the home range of the the jellyfish) only 4% of the protein is unfolded. Heating it up to 30°C, you find that 82% of the protein is now unfolded. Using this information, determine the change in enthalpy for unfolding this protein. For this, you can simplify the calculation by assuming that AH is independent of temperature. (10 pts)

Answer 1

Hi!

Let's discuss thermodynamics.

So, folded or unfolded, what is the difference in energy?

In the folded structure we are told that there is an order in the structure, the hydrophilic functional groups get exposed and the hydrophobic ones "hidden" as facing the interior of the protein and interacting with the other hydrophobic residues. This is a response to the media since the protein is in a hydrophilic environment.

So, for entropy you know is associated with possibilities of rearrangements that have the same energy. If the structure was unfolded the water and ions that surround it could take more configurations whereas in the folded one the water has a designated place to be as we say "order" we mean less configurations available, more structured configuration. So the folded structure will have much less entropy than the unfolded one.

About enthalpy, we have that the folded structure has lower energy, is more stable. Because of the interactions, hydrophobic is interacting with hydrophobic; and hydrophilic with hydrophilic. This interactions contribute to lower the energy whereas in the unfolded structure we'll have repulsive interactions or weaker interactions. So DH would be negative if we go from unfolded to folded and positive if we go from folded to unfolded.

You know that positive DH means endothermic reaction, so it makes sense that when we heat the protein it unfolds.

For B, we'll use Van't Hoff's equation:

Incam! R DH * KT2 T T

$K_{t}=\frac{folded}{unfolded}$

and the percentages are then Kt . 100 so remember to divide by 100.

$ln\left ( \frac{0,82}{0,4} \right )= -\frac{8,314J/Kmol}{DH}*\left ( \frac{1}{(30+273)K}-\frac{1}{(5+273)K} \right )$

DH= 3, 43.10^-3 J/mol

Hope to have been helpful!