Are proteins just coiled cords? Local and Global analysis of Contact Maps reveals the backbone-dependent nature of proteins

In this work, we present an extensive analysis of protein contact network topology applied to a wide data set. We extended the concept of degree distribution to graphlets, describing local connectivity patterns. We compared results to those derived from artificial networks of the same size (number of nodes), reproducing the average degree of each protein network. The artificial networks resemble the coiling of immaterial cords and we tried to understand if they could catch the protein structure topology upon the sole constraint of backbone (cord). We found a surprisingly similar pattern for local topological descriptors (graphlets distribution) while real proteins and cords differ at large extent in the global topological invariant average shortest path that presumably catches the systemic nature of protein and the non egligible encumbrance of backbone (residues steric hindrance). We demonstrated average shortest path to link polymer length and physical size of the molecule, and its minimization plays the role of 'target function' of folding process.