Protein structure and polymer collapse

Scaling relationships and a self-consistent field (SCF) theory of the structure of globular proteins are presented. A large data base is examined which shows that the radius of gyration of a protein Rg scales as Nν, where ν is approximately 1/3. This scaling behavior is predicted for collapsed polymers. Additional justification for polymer collapse conditions is given by an analysis of the fractal dimension of protein backbones. A collection of data also shows that the surface area of proteins S scales as S ∼ Rdsg, where ds equals 2.1. This property is also shown to be consistent with polymer collapse. A detailed SCF theory is presented for a collapsed polymer in which two- and three-body interactions between the segments are considered. The problem is exactly solvable within the SCF level of approximation and analytic solutions are obtained for the configurational distribution function. The distribution function is used to calculate scaling relationships and the free energy of the polymer.