  Protein-protein interactions (protein functionalities) are mediated by water,
which compacts individual proteins and promotes close and temporarily stable
large-area protein-protein interfaces. In their classic paper Kyte and
Doolittle (KD) concluded that the "simplicity and graphic nature of
hydrophobicity scales make them very useful tools for the evaluation of protein
structures". In practice, however, attempts to develop hydrophobicity scales
(for example, compatible with classical force fields (CFF) in calculating the
energetics of protein folding) have encountered many difficulties. Here we
suggest an entirely different approach, based on the idea that proteins are
self-organized networks, subject to finite-scale criticality (like some network
glasses). We test this proposal against two small proteins that are delicately
balanced between alpha and alpha/beta structures, with different functions
encoded with only 12% of their amino acids. This example explains why protein
structure prediction is so challenging, and it provides a severe test for the
accuracy and content of hydrophobicity scales. The new method confirms KD's
evaluation, and at the same time suggests that protein structure, dynamics and
function can be best discussed without using CFF.
