## 3 Results
### Comparative Analysis--Type III Antifreeze Protein and Rad50 Domain of Mre11  
The two ferredoxins presented in this paper exhibit \(RD\) status of their monomers similar to type III antifreeze proteins (or even lower in case of FdII), which are among the best in terms of 3D Gauss function accordance [12]. At the same time biological function of these ferredoxins demands binding of a ligand and formation of a dimer. A type III AFP does neither of this kind of interactions to carry out its own role. This contradiction has led us to the previous section where we have shown that even at a very low (around 0.3 or less) \(RD\) level measured at the global scale, which strongly hints a well-ordered hydrophobic core surrounded by polar residues, hydrophobicity density maps of FdI and FdII show finely detailed discrepancies that can be linked back to areas natively associated with P-L and P-P interaction. Given the above statement, one may ask whether type III AFPs also have similar \(T\) vs. \(O\) map features. To answer it, we analyzed a representative of this family accessible by PDB code 9 MSI. It is naturally a monomer, mostly unstructured, with its size and shape (Figure 1c) slightly resembling FdII (cealign RMSD: 6.61 A/40 aa, 9.11 A/48 aa for FdI). \(RD\) for the whole molecule is 0.29. All its segments also exhibit very strong accordance (Table S1). A striking similarity can be seen between its \(T\) and \(O\) profiles (Figure 10a), especially on the map (Figure 10c) where not a single residue falls outside the accordance stripe (marked by the dashed lines). There are no members of \(D_{2}\), \(D_{3}\), \(B_{2}\) and \(B_{3}\) classes and just three insignificant representatives of class \(B_{1}\), located deeply within the class \(Z\) square: S24, P33 and D36. The accordance classes (C and \(S\)) capture most of the residues at third level with only 2 and 8 of them respectively being at level 1. This shows that even with similar \(RD\) value, hydrophobicity map characteristic of type III AFP is clearly different from the one exhibited by ferredoxins. It correctly signals that a lack of protein-protein and protein-ligand activity should be expected from it. The three proteins investigated so far: FdI, FdII and type III AFP are globular, relatively small and highly accordant with 3D Gauss function (\(RD\approx 0.3\)). To showcase how the presented approach handles a vastly different structure, we also included 1L8D in this analysis. It is the PDB code for Rad50 domain from Mre11-Rad50-Nbs1 complex. Its hairpin shape and exposition of all residues to the solvent nearly guarantees that no stable hydrophobic core will be found in it (Figure 1d). The same can be said for its dimer. Monomers interact only by their hook regions surrounding the Zn\({}^{2+}\)/Hg\({}^{2+}\) ion, with long helices facing away from each other. This results in a large 3D Gauss capsule with a compact, 14-residue P-P contact area (D429, T432, A433, E436, K439, C444, P445, V446, C447, R449, E450, L451, L459 and Y463) that does not allow most of the complex substrates to share a lot of hydrophobicity. Global \(RD\) values corroborate these assumptions: 0.70 for monomer, 0.67 for dimer and 0.68 for monomer as part of dimer. With the exception of two very short 2-aa beta strands, all segments of Rad50 are also discordant (Table S2). This results in hydrophobicity profile shown in Figure 10b. Distribution differences are clearly visible here, with \(O\) in the hook region prominently towering over very low \(T\). Its two highest peaks are C444 and C447 which coordinate the zinc/mercury ion. They are class \(D_{3}\) members, surrounded by their \(D_{2}\) neighbors: V446, G448 and L451, among which only G448 is not engaged in P-P interaction (Figure 10d). L399, L402, I491 and I495 located at the termini belong to class \(D_{1}\) (9 total) and suggest--although not as strongly--a putative interaction area there.