## 5 Results II: IFP family
### From tetrameric to dimeric form  
We now consider putative SDPs of the tetrameric vs. dimeric form of IFP and analyze some new mutations. To that end, two groups of 13 dimers and 53 tetramers, again sharing the same interface as in DsRed, (\(44.2\%\) and \(52.9\%\) average identity, respectively) were selected from the alignment and underwent our procedure. Comparison between experiments and our results, reported in Table 7, is limited by the fact that the literature focuses on the generic distinction between monomers and multimers and that tetramer-to-monomer and tetramer-to-dimer roles very likely overlap. Out of the first 20 most significant positions predicted by the various flavours of the method implemented in SDPhound, including the BLOSUM based ones due to their potentially innovative character, we selected those not yet tried in experiments. Then, we investigated with the pigeonholing procedure (Table 8) the physical features influencing their specificity. We focused on position 158 since it ranks as the best non experimentally validated position in Table 7 that also belongs to the tetramerization interface in DsRed homologs. The results concerning SDP 158 in Table 8 indicate that dimerization is favoured by changes in size and, to a lesser extent, in charge. In particular, inspection of the sequences revealed that aspartic acid appears only in the dimeric class at position 158 (DTRKCI vs. TRKIV), leading us to select the K158D mutation as a promising candidate to further weaken dimer-dimer binding. We decided to obtain a further assessment of this mutation, validating it independently with the MMPBSA technique [10], a well-established and quite powerful tool to estimate binding free energies such as those involved in oligomerization processes. In this context, free energy is evaluated as an average over molecular dynamics trajectories of \(G=E_{MM}+G_{PB,polar}+G_{SA,nonpolar}-TS_{solute}\). Details concerning the meaning of the individual terms, the implementation and the actual calculation can be found in the SI. Here, we only point out that binding free energy \(\Delta G_{i}\) can be estimated for each mutant as the free energy difference between tetramers and dimers, so that \(\Delta\Delta G_{i,WT}\) is the binding free energy difference of the \(i^{th}\) mutant with respect to WT DsRed. To benchmark MMPBSA, we created, _in silico_, three mutants, namely I125R/V127T, dimer2* and mRFP1* (see caption of Figure 4 for details), for which the tetrameric character can be confidently excluded (\(\Delta\Delta G_{i,WT}>0\)). Despite the rather short length (400 ps) of the dynamics (hence the relatively large error bars), the calculations, shown in Figure 4 together with the details about exact mutations, reproduce the expected trends and support the ability of the I125R mutation to disrupt the tetramer (\(\Delta\Delta G_{I125R/V127T,WT}\)=40.79 kcal/mol), consistently with what described in [27]. For dimer2* and mRFP1* we report slightly lower values (\(\Delta\Delta G_{dimer2^{*},WT}\)=26.69 kcal/mol and \(\Delta\Delta G_{mRFP1^{*},WT}\)=23.23 kcal/mol) than for the I125R/V127T mutant; this is reasonable since in those cases mutagenesis introduced many mutations that, in addition to providing control over oligomerization tendency, preserved other essential properties, such as correct and fast protein folding, chromophore maturation and detectable fluorescence. More interesting is the study of the tetramerization free energies of K158D mutant as well as the physical insights that emerge. \(\Delta\Delta G_{K158D,WT}\)=26.67 kcal/mol actually indicates a very promising mutation, not likely to affect the fluorescence due to the location of the residue far from the chromophore.