Hidden valley structure of Ising spin glasses

Energy landscapes, supergraphs, and "folding funnels" in spin systems

Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of the system in a unified coarse-grained sense. We give examples of the supergraphs for several two-dimensional spin and protein-related systems. We demonstrate that disordered ferromagnets have supergraphs akin to those of model proteins whereas spin glasses behave like random sequences of amino acids that fold badly.

Cell dynamics of folding in two-dimensional model proteins

BACKGROUND

Functionally useful proteins are sequences of amino acids that fold rapidly under appropriate conditions into their native states. It is believed that rapid folders are sequences for which the folding dynamics entail the exploration of restricted conformations-the phase space can be thought of as a folding funnel. While there are many experimentally accessible predictions pertaining to the existence of such funnels and a coherent picture of the kinetics of folding has begun to emerge, there have been relatively few simple studies in the controlled setting of well-characterized lattice models.

RESULTS

We design rapidly folding sequences by assigning the strongest couplings to the contacts present in a target native state in a two-dimensional model of heteropolymers. Such sequences have large folding transition temperatures and low glass transition temperatures. The dependence of median folding times on temperature is investigated. The pathways to folding and their dependence on the temperature are illustrated via a study of the cell dynamics-a mapping of the dynamics into motion within the space of the maximally compact cells.

CONCLUSIONS

Folding funnels can be defined operationally in a coarse-grained sense by mapping the states of the system into maximally compact conformations and then by identifying significant connectivities between them.