Characterizing Protein Shape by a Volume Distribution Asymmetry Index

A fully quantitative shape index relying upon the asymmetry of mass distribution of protein molecules along the three space dimensions is proposed. Multidimensional statistical analysis, based on principal component extraction and subsequent linear discriminant analysis, showed the presence of three major 'attractor forms' roughly correspondent to rod-like, discoidal and spherical shapes. This classification of protein shapes was in turn demonstrated to be strictly connected with topological features of proteins, as emerging from complex network invariants of their contact maps.