Two State Behavior in a Solvable Model ofβ-Hairpin Folding

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here we describe a simple model for the formation of a $\beta$ hairpin, motivated by the fact that folding of a $\beta$ hairpin captures much of the basic physics of protein folding. The modeled hairpin is composed of two interacting Gaussian chains with one pairwise (two-body) and two many-body interactions. We show that these many-body interactions, arising from side chain packing effects, are responsible for producing an “all-or-none” folding transition. We also estimate the (single exponential) folding/unfolding rate via calculating the thermodynamic weight of the “critical” droplet/bubble.