Questions for Plaxco et al. paper
For every protein,
you can define its residueresidue contact map,
which is simply a matrix A
with entries a[i][j] equal to 1
if residues (amino acids) i and j touch each other and
0 otherwise.
Amino acids are labeled sequentially in the polypeptide chain.

Question 1.
Can a strictly diagonal matrix
(e.g., a[i][j] equals 1 if and only if i=j)
represent a real protein?
Explain.

Question 2.
You have two proteins,
X and Y,
each made of exactly 100 amino acids.
X has a residueresidue contact map
with i,jth entry 1 if and only if ij<6.
Y has a residueresidue contact map
with i,jth entry 1 if and only if ij<5 or ij=95.
According to Plaxco et al.,
which protein will have a faster rate of folding?
Explain

Question 3.
Is it likely that a functional enzyme protein in its native state has
a residueresidue contact map
A such that a[i][j]=1 if and only if
ij=0 or =1?
Explain.

Question 4.
A 100x100 matrix A is defined
as a[i][j]=1 if and only if
ij<6 or i=25.
Can this be the residueresidue contact map of a real protein?
Explain.

Question 5.
Assume that the theory of Plaxco et al. applies to polypeptides as well
(these can be thought of as very small proteins).
Based on the theory,
order the following four polypeptides by their folding times:
a) 24residue alpha helix, "a24";
b) 48residue alpha helix, "a48";
c) 24residue beta hairpin "b24";
and d) 48residue beta hairpin "b48".
If you want to know more about contact maps and
are curious what a contact map of a real protein from the PDB site
looks like,
you may
download the Macromolecular Contact tool and play with it.
It is Javabased and should be pretty much plugandplay.
Note.
No rigorous proofs are required, just good, qualitative logic.