Scaling Law for the Radius of Gyration of Proteins and Its Dependence on Hydrophobicity

The scaling law between the radius of gyration and the length of a polymer chain has long been an interesting topic since the Flory theory. In this article, we seek to derive a unified formula for the scaling exponent of proteins under different solvent conditions. The formula is obtained by considering the balance between the excluded Volume effect and elastic interactions among monomers. Our results show that the scaling exponent is closely related to the fractal dimension of a protein's structure at the equilibrium state. Applying this formula to natural proteins yields a 2/5 law with fractal dimension 2 at the native state, which is in good agreement with other studies based on Protein Data Bank analysis. We also study the dependence of the scaling exponent on the hydrophobicity of a protein chain through a simple two-letters HP model. The results provides a way to estimate the globular structure of a protein, and could be helpful for the investigation of the mechanisms of protein folding. (C) 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 207-214, 2009