Statistical Properties of Contact Maps

TL;DR

This paper investigates the exponential growth and statistical properties of contact maps in protein structures, using exact enumeration methods on various lattice models to understand their combinatorial complexity.

Contribution

It provides the first detailed enumeration and analysis of contact maps for polypeptide chains on different lattice structures, revealing their exponential growth and statistical characteristics.

Findings

Number of contact maps grows exponentially with chain length for D>1

Exact enumeration results for 2D square and triangular lattices up to 20 steps

Statistical properties of contact maps on ladder models analyzed

Abstract

A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the possible configurations of a polypeptide chain of N amino acids, represented by (N-1)-step self avoiding walks on a lattice, grows exponentially 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 corresponding to such walks. We also study the exact statistics of contact maps generated by walks on a ladder.