Heteropolymer freezing and design: Towards physical models of protein folding

Protein folding has become one of the most actively studied problems in modern molecular biophysics. Approaches to the problem combine ideas from the physics of disordered systems, polymer physics, and molecular biology. Much can be learned from the statistical properties of model heteropolymers, the chain molecules having different monomers in irregular sequences. Even in highly evolved proteins, there is a strong random element in the sequences, which gives rise to a statistical ensemble of sequences for a given folded shape. Simple analytic models give rise to phase transitions between random, glassy, and folded states, depending on the temperature T and the design temperature $T^{\mathrm{des}}$ of the ensemble of sequences. Besides considering the analytic results obtainable in a random-energy model and in the Flory mean-field model of polymers, the article reports on confirming numerical simulations.