Controversial Nano-Cages:

Recently, the Heddle lab have generated a spherical like assembly of TRAP proteins made out of 24 regular faces, each made out of 11 TRAP proteins. We call the structure a cage because it also has 38 small holes. That geometry is known to be mathematically impossible, so to elucidate this mystery, we have generated mechanical models of such cages and showed that they are realisable if one allows for a 0.5% deformation of the edges and the angles of the polygonal faces Nature 569 (2019) 438-442 doi 10.1038/s41586-019-1185-4.

24 hendecagons (11 edges polygon) forming a nearly regular cages. Edges and angles of each face are at most 0.5% different from a perfectly regular hendecagon 12 hendecagons (11 edges polygon) forming a nearly regular cages. Edges and angles of each face are at most 1.8% different from a perfectly regular hendecagon


The motivation to generate such protein cages is to create nano-containers into which drugs can be trapped for targeted delivery [2]: by fitting some of the cage holes with specific receptors, one can target specific cells, like cancer cells, reducing both the amount of drug needed, hence reducing cost, but also limiting the drug's sides effects.

To form such cages one must use a protein which polymerises to form polygons, also named "rings" because they exhibit a small hole at the centre, and these rings must then polymerise together to form a cage (via some linkers which are part of the protein design.) A key question is then how many edges/components a ring much have to be able to form a cage. The outside edges of the rings must also be tapered so that the angles between them matches that of the cages that are formed. There is thus a call to catalogue all the possible cages together with their properties so that bio-chemists can identify potential proteins for cage formation. Together with J. Heddle, Agnieszka Kowalczyk and myself are determining all the possible geometries corresponding to nearly symmetric cages. This is work in progress but some preliminary results were published the the proceedings of the Bridges 2019 conference