## 3 Results and Discussion  
### Residue Propensities  
Based on our definition of surface and contact atoms, the number of occurrence of each of the 20 amino acids (AA) were calculated in the whole set, the set of surface atoms and the set of contact atoms. The results are in Table 1, with AAs arranged in the order of hydrophobic, polar, charged. Columns 1, 2, and 4 of Table 1 show the percent of time each residue occurred in the dataset (all), on the surface (surf) or among the contact atoms (cont), resp. Note that uniformly distributed residues would all show up with 5%. Column 3 shows the ratio of surface and overall propensities; not surprisingly the excess  
Figure 1: Schematic showing the relation between mutual proximity and contact. Arrows from one component (filled circles, full line) to the other component (open circles) show the nearest atom in the other set; arrows with broken line show the nearest atom in the first set. The two-headed thick arrow shows the mutually proximal pair.  
likelihood of being on the surface increases moving from the hydrophobic to the charged residues. Residues participating in multiple contacts were only counted once.  
Columns 5 and 6 of Table 1 show the ratios %(cont)/%(all) and %(cont)/%(surf), resp. It is the last column that gives the most striking result: there are significant differences between the contact forming propensities of surface residues. All three aromatic AAs are strong contact formers but so are MET, CYS and HIS. Interestingly, of the charged residues only ARG shows significant contact forming propensity. Recent work showed that \"hot spots\" of protein-protein interactions frequently contain tryptophan, arginine, and tyrosine--this is in accordance with their larger contact-forming propensities found in the present study [26].  
Table 2 shows the contact-pair forming propensities of AA pairs. The table values are normalized by the surface propensities of the contributing residues:  
\[PR_{i,j}=\frac{N_{i,j}}{\sum_{i,j=1}^{20}N_{i,j}}/[P_{i}*P_{i}*(2-\delta_{i,j})]\]  
where \(PR_{i,j}\) is the propensity of the residue pair \(\{i,j\}\) to form contact, \(P_{i}\) is the probability of residue \(i\) being on the surface, \(N_{i,j}\) is the number of \(\{i,j\}\) pairs found in the data set and \(\delta_{i,j}\) is the Kronecker delta (one when \(i=j\), zero otherwise). This means that if a residue does not have any preference for contacting residues then the entries involving that residue should be all ones. \(PR_{i,j}\) values over 3.0 are highlighted in bold type  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **\%(all)** & **\%(surf)** & **\%(surf)/\%(all)** & **\%(cont)** & **\%(cont)/\%(all)** & **\%(cont)/\%(surf)** \\ \hline GLY & 6.97 & 6.32 & 0.91 & 5.27 & 0.76 & 0.83 \\ ALA & 6.83 & 5.42 & 0.79 & 4.55 & 0.67 & 0.84 \\ VAL & 6.80 & 5.03 & 0.74 & 5.23 & 0.77 & 1.04 \\ LEU & 8.72 & 6.45 & 0.74 & 6.47 & 0.74 & 1.00 \\ ILE & 5.33 & 3.96 & 0.74 & 4.79 & 0.90 & 1.21 \\ PHE & 3.70 & 2.89 & 0.78 & 4.24 & 1.15 & 1.47 \\ TRP & 2.10 & 2.11 & 1.00 & 2.98 & 1.42 & 1.41 \\ TYR & 4.07 & 4.31 & 1.06 & 6.23 & 1.53 & 1.44 \\ PRO & 5.08 & 5.62 & 1.11 & 5.50 & 1.08 & 0.98 \\ MET & 1.81 & 1.58 & 0.87 & 2.22 & 1.22 & 1.40 \\ SER & 5.88 & 6.19 & 1.05 & 5.17 & 0.88 & 0.83 \\ THR & 6.13 & 6.51 & 1.06 & 5.58 & 0.91 & 0.86 \\ CYS & 1.83 & 1.13 & 0.62 & 1.58 & 0.86 & 1.39 \\ ASN & 4.21 & 4.86 & 1.16 & 5.09 & 1.21 & 1.05 \\ HIS & 2.39 & 2.68 & 1.12 & 3.60 & 1.50 & 1.34 \\ GLN & 4.62 & 5.62 & 1.22 & 6.02 & 1.30 & 1.07 \\ ASP & 5.53 & 6.65 & 1.20 & 6.11 & 1.10 & 0.92 \\ GLU & 6.81 & 8.44 & 1.24 & 6.15 & 0.90 & 0.73 \\ LYS & 6.43 & 8.25 & 1.28 & 5.87 & 0.91 & 0.71 \\ ARG & 4.76 & 5.97 & 1.25 & 7.36 & 1.55 & 1.23 \\ \hline \end{tabular}
\end{table}
Table 1: Residue propensities to appear (all), be on the surface (surf) or form contact (cont).