# Fractal Aspects of Human S100 Protein Structures
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**S100 Protein** & **PDB ID** & **Mutation** & **D\({}_{\rm s}\)** & **Predicted** & **Polar Surface** & **Apolar Surface** \\  & & & & **Conformation** & **Area (Å\({}^{2}\))** & **Area (Å\({}^{2}\))** \\ \hline \multirow{8}{*}{S100B} & 2 PRU & - & 2.392 & E & 4099.66 & 5284.99 \\  & 1 UWO & - & 2.432 & E & 4659.90 & 5458.57 \\  & 1 MQ1 & - & 2.427 & E & 4326.62 & 5672.52 \\  & 2 MQ49 & - & 2.177 & E & 4970.71 & 5694.94 \\  & 3 DOY \({}^{*}\) & - & 2.296 & E & 3642.37 & 5585.78 \\  & 3D10 \({}^{*}\) & - & 2.234 & E & 4030.30 & 6016.60 \\  & 3 HCM \({}^{*}\) & - & 2.324 & E & 3992.63 & 5783.58 \\  & 5 CSI \({}^{*}\) & - & 2.207 & E & 3479.18 & 5846.94 \\ \hline \multirow{2}{*}{S100P} & 1 OZO & - & 2.225 & E & 2933.71 & 5805.56 \\  & 2 MJW & - & 2.297 & E & 3501.60 & 6270.19 \\ \hline \hline \end{tabular}  
* The mean value of the surface fractal dimension is D\({}_{\rm s}\) = 2.35 \(\pm\) 0.09 for solution structures and D\({}_{\rm s}\) = 2.23 \(\pm\) 0.05 for crystal structures, both revealing the complexity of the human S100 protein surfaces.  
\end{table} 
Table 1: _Cont._There are small differences in the values of surface fractal dimensions obtained for the structures of the same protein in apo- and calcium- or -sodium loaded form, respectively, for the structures of protein complexes with different ligands (Table 1). In addition, there are also differences between the surface fractal dimension values for the structures corresponding to the native protein and its mutants, underscoring the role of mutations in altering protein structures and modulating responses to calcium fluctuations (Table 1). Changes in the structures of the investigated S100 proteins due to calcium and/or ligand binding, respectively, due to mutations in the protein sequences are also highlighted by superimposing the structures (Supplementary Table S2). In cases of S100A1, S100A2, S100A5, and S100A13, the proteins adopt more compact or smoother conformations in the presence of calcium or of the ligand, resulting in a decrease in the surface fractal dimension. In the case of the S100A1 protein, its surface fractal dimension decreases from 2.404 in apo-form (PDB ID 2L0P) to 2.324 in calcium-loaded form (PDB ID 2 LP2). This is in good correlation with structural data revealing that after calcium binding, S100A1 undergoes an important conformational change, resulting in the exposure of a large hydrophobic cleft that binds to target proteins [47]. For S100A2, there is a decrease in the surface fractal dimension from 2.293, obtained for the sodium-loaded structure (PDB ID 2 RGI), to 2.259 for the calcium-loaded structure (PDB ID 4 DUQ), revealing the influence of the cation type. For the S100A5 protein, the surface fractal dimension decreases from 2.264 in apo-form (PDB ID 2 KAX) to 2.181 in calcium-loaded form (PDB ID 2 KAY). The 2 KAX and 2 KAY structural files, corresponding to S100A5 in apo- and calcium-loaded forms, respectively, reveal structural differences resulting from calcium binding, leading to a change in the overall shape of the protein from spherical to extended (Table 1) and changes in the distribution of hydrophobic and charged residues of the S100A5 homodimer [48]. For S100A12, the surface fractal dimension increases from 2.215 for the sodium-loaded structure (PDB ID 2 WCE) to 2.184 for the calcium-loaded structure (PDB ID 1E8A), also revealing the influence of the type of ion bound on the surface properties. In the case of the S100A13 protein, its surface fractal dimension decreases from 2.288 (PDB ID 1 YUS) in apo-form to 2.251 in calcium-loaded form (PDB ID 1 YUU). Structural data for the S100 protein also show that the binding of two calcium ions per monomer generates key conformational changes [49]. All these changes reveal that these protein surfaces become more ordered upon calcium binding and that there are differences in the effects of various ions binding on the surface properties.