  We propose a universal elastic energy for proteins, which depends only on the
radius of gyration $R_{g}$ and the residue number $N$. It is constructed using
physical arguments based on the hydrophobic effect and hydrogen bonding.
Adjustable parameters are fitted to data from the computer simulation of the
folding of a set of proteins using the CSAW (conditioned self-avoiding walk)
model. The elastic energy gives rise to scaling relations of the form
$R_{g}\sim N^{\nu}$ in different regions. It shows three folding stages
characterized by the progression with exponents $\nu = 3/5, 3/7, 2/5$, which we
identify as the unfolded stage, pre-globule, and molten globule, respectively.
The pre-globule goes over to the molten globule via a break in behavior akin to
a first-order phase transition, which is initiated by a sudden acceleration of
hydrogen bonding.
