# Questions for Plaxco et al. paper

For every protein, you can define its residue-residue 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 residue-residue contact map with i,jth entry 1 if and only if |i-j|<6. Y has a residue-residue contact map with i,jth entry 1 if and only if |i-j|<5 or |i-j|=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 residue-residue contact map A such that a[i][j]=1 if and only if |i-j|=0 or =1? Explain.

• Question 4. A 100x100 matrix A is defined as a[i][j]=1 if and only if |i-j|<6 or i=25. Can this be the residue-residue 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) 24-residue alpha helix, "a24"; b) 48-residue alpha helix, "a48"; c) 24-residue beta hairpin "b24"; and d) 48-residue 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 Java-based and should be pretty much plug-and-play.

Note. No rigorous proofs are required, just good, qualitative logic.