A mathematical framework for the classification of Self-assembling Polypeptide Nanoparticles
Giuliana Indelicato, University of Torino

In the last decade scientists have started engineering many different self-assembling protein nanoparticles. The possible applications are manifold and innovative: from vectors for the delivery of genes or drugs to synthetic vaccines. The fast development of this research field poses new challenges for the structural analysis as, in general, synthetic nanoparticles do not fit into the Caspar and Klug’s framework: an original approach is needed to provide blueprints for the experimental determination of their structure. We focus on a *de novo *class of proteins, referred to as self-assembling protein nanoparticles (SAPNs). This is a family of nanoparticles that provide a versatile platform for synthetic vaccines against a broad range of diseases, including malaria, SARS, influenza and HIV. These nanoparticles self assemble from multiple copies of a polypeptide synthesized to have specific connectivity properties. The polypeptides bind to each other following precise local assembly rules, forming groups of five or three polypeptides. To elucidate the resulting assembled global structure, we use tools from graph theory. This approach unveils a hidden relation with fullerene geometries and enables a full classification of the high and low symmetry particles observed in experiments.