Protein folding as a jamming transition

Proteins fold to a specific functional conformation with a densely packed hydrophobic core that controls their stability. We develop a geometric, yet all-atom model for proteins that explains the universal core packing fraction of ${\varphi }_c=0.55$ found in experimental measurements. We show that as the hydrophobic interactions increase relative to the temperature, a novel jamming transition occurs when the core packing fraction exceeds ${\varphi }_c$ . The model also recapitulates the global structure of proteins since it can accurately refold to native-like structures from partially unfolded states.