Proteins as networks: Usefulness of graph theory in protein science

The network paradigm is based on the derivation of emerging properties of studied systems by their representation as oriented graphs: any system is traced back to a set of nodes (its constituent elements) linked by edges (arcs) correspondent to the relations existing between the nodes. This allows for a straightforward quantitative formalization of systems by means of the computation of mathematical descriptors of such graphs (graph theory). The network paradigm is particularly useful when it is clear which elements of the modelled system must play the role of nodes and arcs respectively, and when topological constraints have a major role with respect to kinetic ones. In this review we demonstrate how nodes and arcs of protein topology are characterized at different levels of definition: 1. Recurrence matrix of hydrophobicity patterns along the sequence 2. Contact matrix of alpha carbons of 3D structures 3. Correlation matrix of motions of different portion of the molecule in molecular dynamics. These three conditions represent different but potentially correlated reticular systems that can be profitably analysed by means of network analysis tools.