In their seminal 1956 Nature paper, Francis Crick and James Watson proposed that the surface structures of viruses were produced from a limited number of protein building blocks, by using the principle of symmetric self-assembly. The ensuing years of biophysical research identified myriads of oligomeric proteins that assemble using such symmetry rules. Some proteins use polyhedral symmetry (tetrahedral, octahedral, or icosahedral) to create cage or shell-like architectures, which serve as storage, catalysis, structural scaffolding, or as enclosures for viral genomes. Our paper in the February 2 issue of BJ focuses on a de novo class of proteins, referred to as self-assembling protein nanoparticles (SAPNs). SAPNs are assembled from monomeric protein building blocks, covalently attached to antigens from pathogens, to create simple, potent, and cost-effective vaccines. The SAPN malaria vaccine candidate is currently going into the phase of clinical testing. The protein assemblies can also be modified for the delivery of functional peptides, or encapsulation of nanoparticles such as gold or quantum dots, for imaging and therapeutic uses.

The symmetric classification of different particle morphologies of SAPNs have been predicted via a mathematical formalism known as tiling theory. Reidun Twarock, a mathematical biophysicist at the University of York, pioneered the use of tiling theory in virology to solve a long-standing problem regarding the structure of the cancer-causing polyomaviridae, which exhibit more than the 12 pentagonal protein clusters expected in Donald Caspar and Aaron Klug’s classification of virus architecture.We adapted the tiling approach o model protein nanoparticles with a mixture of local 5- and 3-fold symmetry axes. In combination with electron microcopy and neutron scattering data, our classification of surface structures made it possible to identify particle morphologies that have been difficult to identify using experimental methods alone.

The cover image is an artistic interpretation of six SAPNs, five of which have been identified by the new mathematical classification. The local symmetry building blocks of the SAPNs are represented by a pentagon (5-fold axis or pentameric building block) with internal triangles (3-fold axis or trimeric building block). The middle particle, centered on the face of a pentagon, is a sixty chain oligomer which assembles according to the known icosahedral symmetry of small viruses. The other five symmetric particles, increasing in size by an order of sixty chains and centered on the vertices of a pentagon, represent extensions of tiling theory that are introduced in the paper. The nanoparticles are depicted in an aqueous solution, which takes the form of Fibonacci spirals.  The goal of the artwork is to highlight the inherent symmetry principles guiding the assembly of the protein particles, and to maintain a focus on the important role of mathematics in bio-nanotechnology. The art was created by Lauren Brunk, Annie DeGraff, Newton Wahome (adaptation of Fibonacci Pentagon by Alberto Almarza).

—Newton Wahome, Giuliana Indelicato, Philippe Ringler, Shirley A. Müller, Mu-Ping Nieh, Reidun Twarock, Peter Burkhard