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

TL;DR

This paper introduces supergraphs that combine dynamical transition rates and energy landscapes in spin systems, providing insights into their folding behavior and static properties.

Contribution

It presents a unified supergraph framework for analyzing both dynamics and statics in spin systems, including disordered ferromagnets and spin glasses.

Findings

Disordered ferromagnets have supergraphs similar to model proteins.

Spin glasses behave like random amino acid sequences.

Supergraphs reveal differences in folding and energy landscape complexity.

Abstract

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 aminoacids which fold badly.