Questions for Plaxco et al. paper


For every protein you can define its residue-residue ``contact map" which is simply a matrix (A) such that a[i][j] = 1 if residues (amino acids) i and j touch each other and zero otherwise. Naturally, you assume that amino-acids are labelled sequentially in the polypeptide chain.

Q1 Can a strictly dioganal matrix e.g. a[i][j] = 1 only if i=j (and zero otherwise) represent a real protein? Explain.

Q2 You have two proteins, X and Y, each made of exactly 100 amino-acids. Protein-X has (A) such that a[i][j] = 1 if |i - j| < 6; a[i][j] = 0 otherwise. Protein-Y is such that a[i][j] = 1 if |i - j| < 5 OR |i - j | = 95; a[i][j] = 0 otherwise. According to Plaxco et al., which protein will have faster rate of folding and why?

Q3 Is it likely for a functional enzyme protein in its native state to have (A) such that a[i][j] = 1 only if |i - j| = 0 or 1? Explain.

Q4 A 100x100 matrix A is defined as a[i][j] = 1 if |i - j| < 6 OR if i=25; a[i][j] = 0 otherwise. Can this be the contact matrix (map) of a real protein? Explain.

Q5 Assume that the theory of Plaxco et al. applies to polypeptides as well (these can be considered 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 might look 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 required, just good, qualitative logic.