Fractal Aspects of Human S100 Protein Structures

This study analyzes the fractal aspects of the structures of S100 proteins to better understand their structural complexity. We take into account 33 solution structures and 18 crystal structures corresponding to human S100 proteins for the calculation of mass and surface fractal dimensions. The mass fractal dimension value is calculated as Dm = 1.54, confirming the extended conformation of the dimers of these proteins. The mean value of the surface fractal dimension is Ds = 2.35 ± 0.09 when computed using solution structures and Ds = 2.23 ± 0.05 when computed using crystal structures, revealing the surface irregularities of S100 proteins. Changes in surface fractal dimensions have been recorded for S100 proteins due to the changes in the pH of the environment, due to mutations in their sequences that alter how the protein folds, and/or due to their interactions with ions and/or ligands that reflect the structural rearrangements that occur upon binding. These changes can significantly influence the biological activity of the protein, making the fractal dimension of the surface a valuable parameter in studying protein functions, interactions, and potential therapeutic targeting.