Entropic Barriers, Frustration, and Order: Basic Ingredients in Protein Folding

We consider the intrinsic entropy and energy barriers of cross-linking in a set of $M$ monomers, plus minimal kinetic restrictions on the folding process of a proteinlike molecule. For a finite-size chain, there is an effective folding transition to an ordered structure. Without frustration, this state is reached in a time that scales as $M^{\lambda }$, with $\lambda \simeq 3$. This scaling is limited by the amount of frustration which leads to the dynamical selectivity of proteins in a well defined range of temperatures, and $M\lesssim 300$ monomers. These predictions resemble generic properties of in vivo globular proteins.