  Protein nanoparticles play pivotal roles in many areas of bionanotechnology,
including drug delivery, vaccination and diagnostics. These technologies
require control over the distinct particle morphologies that protein
nanocontainers can adopt during self-assembly from their constituent protein
components. The geometric construction principle of virus-derived protein cages
is by now fairly well understood by analogy to viral protein shells in terms of
Caspar and Klug's quasi-equivalence principle. However, many artificial, or
genetically modified, protein containers violate this principle, because
identical protein subunits do not interact in quasi-equivalent ways, leading to
gaps in the particle surface. We introduce a method that exploits information
on the local interactions between the assembly units, called capsomers, to
infer the geometric construction principle of these nanoparticle architectures.
The predictive power of this approach is demonstrated here for a prominent
system in nanotechnology, the AaLS pentamer. Our method not only rationalises
hitherto discovered cage structures, but also predicts geometrically viable
options that have not yet been observed. The classification of nanoparticle
architecture based on the geometric properties of the interaction network
closes a gap in our current understanding of protein container structure and
can be widely applied in protein nanotechnology, paving the way to programmable
control over particle polymorphism.
