Download HW #6 BP401/P475 Fall 2015 Assigned Fr 10/02/15: due: Thursday

HW #6 BP401/P475 Fall 2015 Assigned Fr 10/02/15: due: Thursday 10/08/15 Paul Selvin
1. Explain why a peptide (say, 5-10 or amino acids) doesn’t fold into a well-defined
state, whereas a protein does.
2. The G of a protein is typically a just negative ~5-10 kBT. Explain this in terms of E
and S. Why are, or are-not, the various weak bonds (van Der Waals, hydrogen,
ionic bonds…) important in terms of a protein folding?
3. Explain what happens when you heat up an egg to near boiling, and then bring it
back down to room temperature.
a. Why isn’t the process reversible? You end up with a highly scattering (white)
albumin, whereas it started out clear.
b. Explain in terms of what’s happening to the bonds (primary, secondary, tertiary,
quaternary) and in terms of H, S, G.
c. A student asked me an interesting question. When you heat a protein, how much
more energy are you giving a water molecule? The answer is surprisingly small.
Yet we say that this is enough to break bonds. Is that really true? If so, why?
4. Protein Folding: Energy, Entropy and Gibb’s Free Energy:
Consider the following two-dimensional lattice model for a helical 6-mer peptide.
The configuration drawn below is the native state (correctly folded):
Energy rule: any adjacent pair of amino acids not connected by a backbone bond counts as
connected by a hydrogen bond (2 in the example). Assume each hydrogen bond (shown dotted)
stabilizes the system by an energy (enthalpy) of -500 J, with negative means stabilizing. (-500 J is
for one mole of the molecules.) (Recall, we assume H = E, which is true since we are dealing
with solids and liquids.)
Rotated versions of this peptide do not count as separate structures, and only 90° swing
moves are allowed to go from one structure to another (as in lecture).
a. What is the energy of the helical ground state of this model? What is its configurational
entropy? What is its Gibbs free energy at 275 K and 375 K? There is only one state for this
configuration.
b. Draw all structures that have an energy of –500 J. Label each structure with a choice from
this list: “helix initiating state” or “completely unfolded state” or “off-pathway trap” or
“hairpin state” or “almost hairpin state.” Hint: the total number of structures should be 6.
c. Draw as many structures of unfolded states (E = 0) as you can. What is the Gibbs free energy
of your unfolded ensemble at 275 K and 375 K? Comparing to (a), will this peptide fold to a
helix somewhere in that temperature range? Hint: the total number of structures should be 13.
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HW #6 BP401/P475 Fall 2015 Assigned Fr 10/02/15: due: Thursday 10/08/15 Paul Selvin
d. According to the energy rule, the ground state is actually degenerate! Draw the other low
energy state, and label it with a choice from the list in (b). Is this peptide a good design for
isolated unique secondary structure, according to the energy rule?
e. Secondary structure is never isolated in proteins. Introducing three black circles as
“hydrophobic amino acids,” draw a structure of a perfect amphipathic (having both a
hydrophobic and hydrophilic) helix on the lattice. Let us say such a structure gets an extra
score of –1000 J for having all non-polar amino acids on one side, -500 for having 2 on one
side. Draw the structure of the low energy state in (d) with the same position of the
hydrophobic residues as in the helix. Now what is the energy of the helix vs. the state in (d)?
What secondary structure would this peptide form in the context of a protein, where
hydrophobic residues can be buried if they all lie on one side of the peptide?
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