## 3 Results
### Hydrophobicity-Based Ligand Binding Site and Protein-Protein Interface Determination
However, one can instead plot a 2D hydrophobicity map (\(T\) vs. \(O\)) for a given protein, partition it into segments with size and location depending on the distribution of the residues (specific to this structure) and assign the partitioned residues to feature levels, such as hydrophobic core or a possible protein-protein interaction area. It should be noted that this classification of individual residues is not entirely new. Its first form has been proposed in [44] and modified versions were used throughout some of the other papers [32; 59; 60]. However, here we provide not only a formal definition with description of the calculation algorithm but also introduce some important improvements to use now on, hence its appearance in Results rather than in Methods. A single residue can be assigned to one of five FOD hydrophobicity classes:  
* Class \(C\) (_core_)--hydrophobic core: both \(T\) and \(O\) are relatively high (\(T\!\!\!\uparrow\!\!\uparrow\!\!O\)) and the difference between them is relatively low (\(\,\!\!\!\uparrow\!\!\uparrow\!\!\!O\!\downarrow\!\!\uparrow\!\!\!\uparrow\!\!\! \uparrow\!\!\!O\));
* Class \(S\) (_surf_)--hydrophilic surface: both \(T\) and \(O\) are relatively low  
\(T\) profile, often due to the chain going through the center of the drop) where the visual difference between the distributions could provoke the researcher to assign a \(D\) or \(B\) class, contrary to what the statistic is suggesting. This somewhat paradoxically puts most of class \(C_{2}\) area further away on the map from class \(Z\) square than class \(C_{3}\). Similar situation happens in class \(S\), although there is much lower risk for incorrect assignment by hand here. Automatic classification eliminates any of such problems. Figure 7 presents a six-step residue classification algorithm of FOD, using FdI as an example. This algorithm differs from previously published papers mostly in the definition of level 1 and level 3 assignment, which makes it more flexible. Figure 7: Visualization of algorithm for residue assignment to FOD classes using FdI (1 FXR) monomer as an example: (**a**) calculation of \(T\) distribution thresholds, (**b**) determination of class \(Z\) square vertexes, (**c**) partition of the \(T\) vs. \(O\) space into five segments, (**d**) drawing of helper circles, (**e**) cutting arcs out of helper circles by leaving only their intersection with class \(Z\) square and (**f**) final assignment of residues to classes (\(C\), \(S\), \(D\), \(B\) and \(Z\)) and to their three levels (1, 2, 3). Following steps should be performed in order to classify residues from a given protein structure based on their \(T\) vs. \(O\) hydrophobicity density map:  
1. (Figure 7a) plot residues as points in \(T\) vs. \(O\) space (\(T\) on the X-axis, \(O\) on the Y-axis); calculate quartiles of the \(T\) distribution: Q\({}_{2}\) (median), \(Q_{1}\) (median of \(T<Q_{2}\)) and Q\({}_{3}\) (median of \(T>Q_{2}\)); assign three thresholds: \(T_{1}=Q_{1}\), \(T_{3}=Q_{3}\), \(T_{2}=(Q_{1}+Q_{3})/2\);
2. (Figure 7b) draw a \(T=O\) line and shift it to point [\(T_{1}\),\(T_{3}\)]; draw it again and shift it to point [\(T_{3}\),\(T_{1}\)]; draw a \(T=\) -\(O\) line and shift it to point [\(T_{1}\),\(T_{1}\)]; draw it again and shift it to point [\(T_{3}\),\(T_{3}\)]; four points where pairs of these lines intersect are the class \(Z\) square vertexes: \(v_{cd}\), \(v_{ds}\), \(v_{sb}\) and \(v_{bc}\) (meaning of indexes is explained in point 5);
3. (Figure 7c) extend lines away from class \(Z\) square vertexes, partitioning the \(T\) vs. \(O\) space into five segments, with class \(Z\) square in the middle of the map;
4. (Figure 7d) place four helper circles symmetrically around class \(Z\) square to cut away portions from it to be used as delimiters for level 1 class zones; each circle has \(T_{3}\)-\(T_{1}\) radius and intersects two nearby class \(Z\) square vertexes (i.e., \(v_{cd}\) and \(v_{ds}\));
5.