Statistical properties of contact maps

A contact map is a simple representation of the structure of proteins and o ther chainlike macromolecules. This representation is quite amenable to num erical studies of folding. We show that the number of contact maps correspo nding to the possible configurations of a polypeptide chain of N amino acid s, represented by (N - 1)-step self-avoiding walks on a lattice, grows expo nentially with N for all dimensions D > 1. We carry out exact enumerations in D = 2 on the square and triangular lattices for walks of up to 20 steps and investigate various statistical properties of contact maps correspondin g to such walks.. We also study the exact statistics of contact maps genera ted by walks on a ladder. [S1063-651X(99)10101-6].