Condensed Matter Seminar

A Network Approach to Protein Folding, and to Packing Problems in General

Prof. Zoltan Toroczkai
University of Notre Dame

Friday, September 21, 2007 - 4:00 P.M., NSH 184

The classical approach to protein folding inspired by statistical mechanics avoids the high dimensional structure of the conformation space by using effective coordinates. Here we introduce a network approach to capture the statistical properties of the structure of conformation spaces. In case of proteins, conformations are represented as nodes of the network, while links are transitions via elementary rotations around a chemical bond. Self-avoidance of a polypeptide chain introduces degree correlations in the configuration network, which in turn lead to energy landscape correlations. Folding can be interpreted as a biased random walk on the conformation network. We show that the folding pathways along energy gradients organize themselves into scale free networks, thus explaining previous observations made via molecular dynamics simulations. We also show that these energy landscape correlations are essential for recovering the observed connectivity exponent, which belongs to a different universality class than that of random energy models. In addition, we predict that the exponent and therefore the structure of the folding network fundamentally changes at high temperatures, as verified by our simulations on the AK peptide (a 20-residue alanine-based peptide with 3 lysines (K)).

We also discuss the applicability of network descriptions to packing problems in general, and discuss in more detail the case of 3-D packing of atomic clusters as studied by J Doye et.al. (at Oxford Univ., UK).