It is clear that there are significant differences between the four scales shown above, with respect to the placement of specific amino acids. 1 &  4 both place cysteine as the most hydrophobic residue, while the other two scales do not. The reason for this difference is the fundamentally different methods used for constructing the scales. Scales 1 &  4 were both constructed by examining proteins with known 3-D structures and defining hydrophobic character as the tendency for a residue to be found inside of a protein, rather than on its surface. Cysteines at the surface tend to be reactive and evolution will try to avoid this.

Scales 2 &  3 are derived from the physicochemical properties of amino acid side chains and therefore more clearly follow the trends that would be expected, on the inspection of amino acid structures.

An excellent review of the various "hydrophobicity" scales (37 in all) that exist is given by Cornette, et al.5. This paper evaluates the various scales and attempts to extract correlations from the various types of data presented by the scales. It is a very mathematical paper, but the second Appendix is a valuable reference for the various types of scales available in the literature. Charton &  Charton offer some insight into why so many scales have developed. In their conclusion of a theoretical study of "hydrophobicity", they state: "Hydrophobicity parameters and log P values show a variable dependence on intermolecular forces and steric effects. It seems very likely that no single hydrophobicity parameter or log P value can represent the complete range of amino acid behavior. There is no special phenomenon denoted by hydrophobicity in amino acids. It is the natural and predictable result of differences in the intermolecular forces between water and the amino acid and those between the amino acid and some other medicum. No "hydrophobic bonds" need to be invoked to account for amino acid behavior."

If counting inside-out distributions, Pro is often seen at the surface and thus counted as hydrophilic, forced marriage. In the experimental scales Proline is either missing, since it is an imino acid it can not be handled the same way as the other amino aicds in the water/octanol experiments, or it comes out rather hydrophobic, as you would expect from its properties.

In scale 2&3 Arginine is ranked as being the most hydrophilic. This results from counting all the H-bonding possibilities of Arg as compared to Lys.

In 1&4 flexibility of Lys versus Arg. Lys has to give up many more degrees of freedom than Arg to go inside the protein. Think of F(olded) in equilibrium with U(nfolded). If you loose mobility you loose energy. If nature need a +-charge inside it will do it. But it does not take Lys (4,5 degrees of freedom lost) but Arg (2,5 degrees of freedom lost). Arg looses less.

In scale 2 &  3 Gly is very different. Effect of blocking groups is larger for smaller residues. This is an entropic effect.

In the video I discuss getting Arg/Lys through a membrane. The same explanation can be used for getting them buried inside a folded protein.

The 'pKa distance' between 4.6 and the pH of the cytosol (6 a 7) is much smaller than the distance between 6 a 7 and pKas of Lys and Arg (10-12). So, it costs less to protonate an Asp or Glu than to deprotonate an Arg or Lys. Further, Asp looses very little side chain entropy when it gets fixed in a position needed for activity.