Abstract
We introduce here a mathematical procedure for the structural classification of a specific class of self-assembling protein nanoparticles (SAPNs) that are used as a platform for repetitive antigen display systems. These SAPNs have distinctive geometries as a consequence of the fact that their peptide building blocks are formed from two linked coiled coils that are designed to assemble into trimeric and pentameric clusters. This allows a mathematical description of particle architectures in terms of bipartite (3,5)-regular graphs. Exploiting the relation with fullerene graphs, we provide a complete atlas of SAPN morphologies. The classification enables a detailed understanding of the spectrum of possible particle geometries that can arise in the self-assembly process. Moreover, it provides a toolkit for a systematic exploitation of SAPNs in bioengineering in the context of vaccine design, predicting the density of B-cell epitopes on the SAPN surface, which is critical for a strong humoral immune response.
Highlights
A promising route in the fight against major disease, such as malaria [1,2], SARS [3], influenza [4], HIV [5] and toxoplasmosis [6], is a novel family of nanoparticle-based vaccines [7,8]
We develop here a classification scheme for self-assembling protein nanoparticles (SAPNs) morphologies in terms of surface tessellations and associated graphs that pinpoint the positions of the protein building blocks in the particle surfaces
We focus here on SAPNs used in vaccine design, with protein building block (PBB) given by pairs of linked helices
Summary
A promising route in the fight against major disease, such as malaria [1,2], SARS [3], influenza [4], HIV [5] and toxoplasmosis [6], is a novel family of nanoparticle-based vaccines [7,8]. Caspar & Klug’s seminal classification scheme of viral architectures [17] relies on a geometric approach, predicting the spectrum of possible virus architectures in terms of the numbers and relative positions of these protein clusters (capsomeres) with reference to spherical surface lattices. This classification has revolutionized our understanding of virus structure, and plays a key role in the interpretation of experimental data in virology. A classification of nanoparticle graphs provides an atlas of SAPN geometries and epitope positions
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