Kavli Affiliate: Rudolf Podgornik
| First 5 Authors: , , , ,
| Summary:
Proteinaceous shells useful for various biomedical applications exhibit a
wide range of anomalous structures that are fundamentally different from
icosahedral viral capsids described by the Caspar-Klug paradigmatic model.
Exploring the Protein Data Bank, we have identified nine different types of
anomalous shells structurally close to flat octagonal quasicrystals. As we
show, these numerous shells have cubic nets cut from short-period approximants
of an octagonal tiling composed of square and rhombic tiles. The approximants
and parent tiling are easily obtained within the Landau density wave approach,
while the nonequilibrium assembly of them can be simulated using the pair
potentials derived from critical density waves. Gluing a polyhedron net and
mapping it onto a spherical surface induces tile distortions, and to reduce
them, we introduce and minimize the effective elastic energy of the system.
Thus, we return quasi-equivalence to previously equivalent tiles. Possible
cubic faceting of the octagonal spherical tilings is discussed in terms of the
topological charge distribution over the tiling vertices. The proposed
structural models describe numerous proteinaceous shells including about half
of the known symmetrical enzymes. Our results constitute a fundamental basis
for further applications of identified octagonal assemblies and can help to
discover and study similar systems in the future.
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