Characterizing Protein Shape by a Volume Distribution Asymmetry Index

Nicola Arrigo1, Paola Paci2, Luisa Di Paola*, 1, Daniele Santoni3, Micol De Ruvo1, Alessandro Giuliani5, Filippo Castiglione4
1 Università Campus Biomedico, 00128 Rome, Italy
2 CNR-Institute of Systems Analysis and Computer Science “Antonio Ruberti”, Bio Math Lab, 00185 Rome, Italy
3 CNR-Institute of Systems Analysis and Computer Science “Antonio Ruberti”, 00185 Rome, Italy
4 CNR-Institute for Computing Applications “Mauro Picone”, National Research Council, 00185 Rome, Italy
5 Department of Environment and Health, Istituto Superiore di Sanità, 00161 - Rome, Italy

© 2012 Arrigo et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Università Campus Bio-medico, via Alvaro del Portillo 21, 00128 Rome, Italy; Tel: ++39 06 225419634; Fax: ++39 0622541456; E-mail:


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.

Keywords: Protein shape, protein contact network, topological indices, principal component analysis.