Proteins as sponges: a statistical journey along protein structure organization principles

The analysis of a large database of protein structures by means of topological and shape indexes inspired by complex network and fractal analysis shed light on some organizational principles of proteins. Proteins appear much more similar to "fractal" sponges than to closely packed spheres, casting doubts on the tenability of the hydrophobic core concept. Principal component analysis highlighted three main order parameters shaping the protein universe: (1) "size", with the consequent generation of progressively less dense and more empty structures at an increasing number of residues, (2) "microscopic structuring", linked to the existence of a spectrum going from the prevalence of heterologous (different hydrophobicity) to the prevalence of homologous (similar hydrophobicity) contacts, and (3) "fractal shape", an organizing protein data set along a continuum going from approximately linear to very intermingled structures. Perhaps the time has come for seriously taking into consideration the real relevance of time-honored principles like the hydrophobic core and hydrophobic effect.