## 5 Results II: IFP family
### Monomerization of multimeric IFP
Overall, pigeonholing in the IFP case once again picks many SPDs experimentally known to be relevant for the monomerization of IFPs; moreover, as will be clear in the following, such procedure once again offers valuable insight into the physical properties underlying the \begin{table}
\begin{tabular}{l r r r r r r r r r r} \hline Pos. & **117** & 83 & **194** & **164** & **192** & 156 & 223 & 175 & 153 & 5 \\ \cline{2-11} hyd & 4 & \(-\) & 1 & 8 & 2 & 3 & 22 & 7 & 15 & \(-\) \\ crg & 3 & \(-\) & 5 & 1 & 8 & \(-\) & 4 & \(-\) & 2 & 7 \\ size & 1 & \(-\) & 2 & 3 & 5 & 4 & 19 & 11 & \(-\) & 21 \\ \hline Pos. & 177 & 224 & 124 & 162 & 147 & 4 & 174 & 72 & 8 & 44 \\ \cline{2-11} hyd & \(-\) & 11 & \(-\) & \(-\) & 34 & \(-\) & \(-\) & \(-\) & 6 \\ crg & \(-\) & \(-\) & \(-\) & 19 & 37 & \(-\) & 6 & 12 & \(-\) & \(-\) \\ size & 9 & 7 & 18 & \(-\) & 13 & 12 & 16 & \(-\) & \(-\) & 15 \\ \hline \end{tabular}
\end{table} 
Table 6: Substitution class based runs over SPDs relevant for multimerization in IFPs family. Ranking and colors as in Table 2.  
role of SDPs, with no other input but the sequence alignment. Hydrophobicity is important for positions 194, 192 and 156. It is apparent that nonpolar residues located at an interface can favor multimerization by decreasing the desolvation penalty of the external surface of the protein; this is the case for F194K or Y194K mutations. Charge is relevant for positions 164, 153, 117, and 223; in particular, mutations such as A164R or Y164R can introduce an electrostatic repulsion between monomers that prevents their aggregation. Steric hindrance can be a third cause for the decrease of the rate of binding between single units and the pigeonholing procedure spots positions 117, 194 and 164. It is worth noting that different physical features can be relevant for the same SDP, as is the case with positions 117, 194 and 164, thus restricting the possible identities of the corresponding residues. A164R mutation can, for instance, disrupt the hydrophobic packing of residues on the surfaces of monomers within a tetramer. In some cases, such as 83 and 8, none of the selected physical properties exhibits a significant score. This suggests that none of the partitionings is able to capture the peculiarity relevant in those last cases and it prompts to find alternatives to an a priori definition of the characteristics of the pigeonholes. With that in mind, the \"optimal automatic pigeonholing\" described in section 3.4. was used to generate new substitution classes. We applied it to the set of 92 sequences analyzed in subsection 5.2., setting the number of bins to 5, aiming to maximize the average mutual information of the 10 best ranking positions, regardless of which they are. The method provided a clear-cut partitioning only for some amino acids, as shown in Figure 3, more information on the run can be found in the caption. The obtained partitioning corresponds partially to the traditional amino acid groupings, such as the Taylor's Venn Diagrams [31]. In particular, ARG and LYS residues are grouped together and the individuality of CYS is revealed. Differences in partitionings, however, would not be new and have already been discussed [13]. Since we maximized the average information content of the 10 best ranking positions, the classes we sketch represent the intermingling of individual amino acid peculiarities that are relevant to the monomerization propensity of IFP; our procedure can also be utilized to focus on the properties of one single position at a time. Figure 3: Results of the “automatic pigeonholing” procedure. The process reduces the alphabet from 20, ignoring the gaps, to 5 symbols (the rows in the table) while maximizing the average mutual information of the 10 best ranking positions. Interestingly, the corresponding reduction in the average information content is remarkably small: from 0.421 to 0.407. The space of possible partitionings was explored with \(2.0\ 10^{6}\) iterations.