Protein cores explore a glassy energy landscape*

Over the last 60 years, the general framework that has emerged to describe protein folding is that proteins fold on a funneled energy landscape to their native state at the global energy minimum via an equilibrium process. However, there have been no accurate estimates of the critical folding rate, above which proteins would fold to disordered states. Since the energy minimum for protein cores should correspond to the maximum density, here we develop a purely geometric model of proteins to generate collapsed proteins that are resistant to further compression. First, we find that the packing fraction of protein cores found for all high-quality x-ray crystal structures (φ ~ 0.55) is only obtained in the limit of fast thermal quenching during compression, suggesting that the core packing obtained in protein x-ray crystal structures does not represent a global minimum in energy, but the least dense, yet mechanically stable collapsed state. Furthermore, exploring the energy landscape using slower thermal quenching reveals that core amino acids can possess significantly higher packing fractions than φ ~ 0.55, while satisfying all of the geometric constraints of high-quality protein x-ray crystal structures. We thus provide evidence for the glassy nature of the protein energy landscape, which has important implications for protein structure, dynamics, and function.