Colloquium on February 13th, 2006

Zoltan Toroczkai
Los Alamos National Laboratory

Conformation networks: An application to protein folding

Authors: Erzsebet Ravasz, Zoltan Toroczkai and Gnana Gnanakaran
Packing problems, atomic clusters, polymers, and the ultimate building blocks of life, proteins, all live in high-dimensional conformation spaces littered with forbidden regions induced by steric constraints. Additional interactions between the components (other than hard-core exclusion) will cause the dynamics to sample only a subset of the full conformation space. These properties make the quantitative characterization of such conformation spaces challenging. Here we use a networks approach to describe these spaces for chain-like objects, in particular proteins. Molecular Dynamics (MD) simulations by Rao and Caflisch on beta3s and its heteropolymers and on homoglycine show that the conformation-space network is scale-free with an exponent of -2. Using the concept of gradient networks we show that the scale-free nature is a universal property due to the bias introduced by the interaction energy of the protein. We argue that the -2 exponent appears at and below the critical temperature when the neighboring basins of local potential minima become kinetically disconnected. Our results are further corroborated by MD simulations on the alpha-helix.