Protein Folding, the Levinthal Paradox and Rapidly Mixing Markov Chains

Abstract

In [20,21], A. Šali, E. Shakhnovich and M. Karplus modeled protein folding using a 27-bead heteropolymer on a cubic lattice with normally distributed contact energies; i.e.

$$ E = \sum\limits_{1 \leqslant i < j \leqslant 27} {B_{ij} \delta \left( {r_{i,j} } \right)} $$

where B_i,j is normally distributed with mean -2 and standard variation 1, r_i,j is Euclidean distance between residues i, j, and δ(r_i,j) = 1 if r_i,j = 1 and i, j are not immediate neighbors in the polypeptide chain (i.e. ∣i - j∣ > 1), else 0.

Research supported by Volkswagen-Stiftung