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 exhibit varying degrees of quasi-equivalence in the interactions between identical protein subunits. They can also contain a subset of protein subunits that do not participate in interactions with other assembly units, called capsomers, leading to gaps in the particle surface. We introduce a method that exploits information on the local interactions between the 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.
Keywords: AaLS pentamer cage; interaction network; protein nanoparticle; surface tiling; symmetry.