|Abstract:|| In this talk I will discuss a mathematical framework that allows to predict and classify the layout of polypeptidic building blocks in synthetized nanoparticles. I will focus on the *de-novo *system called SAPN (self-assembling polypeptide nanoparticles) which self assembles from multiple copies of a polypeptidic building block and has been designed to act as a repetitive antigen display system in a novel generation of vaccines. Clinical trials on a vaccine against malaria based on this technology are due to start soon.
The characterization of these particles by experimental methods only is not sufficient to completely elucidate the morphology of the assembled structure. Moreover, the classical theory of Caspar and Klug for the arrangements of protein clusters in viral capsids cannot be used because the SAPNs particles exhibit more than the twelve pentagonal clusters allowed in such classification. In this presentation I will show that graph-theoretical methods can provide important insights into the geometry of such nanoparticles. I will study and classify the topology of the protein networks using tools from planar graph theory. Special attention will be devoted to symmetric particles,which can be fully described and classified.