Contacts between segments in the random-flight model of polymer chains

The probabilities of single and double contacts, and correlations among contacts were calculated for the random-flight model of a polymer chain. The problem was studied earlier by various authors using the Gaussian statistics of the random-flight chain, which is applicable only for long chains, and for contacts which are formed by pair of residues (i,j) which are far from each other (i.e. |i−j|≫1). We used the exact (non-Gaussian) solution of the random flight model, so that our results are applicable also for residues which are relatively close to each other. We applied the results to close contacts of the β-sheet type and α-helix type in proteins, and compared the exact solutions of the problem with Gaussian approximations.