  We analyzed folding routes predicted by a variational model in terms of a
generalized formalism of the capillarity scaling theory for 28 two-state
proteins. The scaling exponent ranged from 0.2 to 0.45 with an average of 0.33.
This average value corresponds to packing of rigid objects.That is, on average
the folded core of the nucleus is found to be relatively diffuse. We also
studied the growth of the folding nucleus and interface along the folding route
in terms of the density or packing fraction. The evolution of the folded core
and interface regions can be classified into three patterns of growth depending
on how the growth of the folded core is balanced by changes in density of the
interface. Finally, we quantified the diffuse versus polarized structure of the
critical nucleus through direct calculation of the packing fraction of the
folded core and interface regions. Our results support the general picture of
describing protein folding as the capillarity-like growth of folding nuclei.
