Protein Folding: A Perspective From Statistical Physics

ABSTRACT In this paper, we introduce an approach to the protein fold-ing problem from the point of view of statistical physics. Protein folding is a stochastic process by which a polypeptide folds into its characteristic and functional 3D structure from random coil. The process involves an intricate interplay between global geometry and local structure, and each protein seems to present special problems. The first part of this chapter contains a concise discussion on kinetics versus thermodynamics in protein folding, and introduce the statistical physics basis of protein folding. In the second part, we introduce CSAW (conditioned self-avoiding walk), a model of protein folding that com-bines the features of self-avoiding walk (SAW) and the Monte Carlo method. In this model, the unfolded protein chain is treated as a random coil described by SAW. Folding is induced by hydrophobic forces and other interactions, such as hydrogen bonding, which can be taken into account by imposing conditions on SAW. Conceptually, the mathematical basis is a generalized Langevin equation. Despite the simplicity, the model provides clues to study the universal aspects while we overlook details and concentrate only on a few general properties. To illustrate the flexibility and capabilities of the model, we consider several ex-amples, including helix formation, elastic properties, and the transition in the folding of myoglobin. From the CSAW simulation and physical arguments, we find a universal elastic energy for proteins, which depends only on the radius of gyration Rg and the residue number N. The elastic energy gives rise to scaling laws Rg ∼ Nν in different regions with exponents ν = 3/5, 3/7, 2/5, consistent with the observed unfolded stage, pre-globule, and molten globule, respectively. These results indicate that CSAW can serve as a theoretical laboratory to study universal principles in protein folding. 1 a