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The architectural elements of four protein cages (bacterio ferritin, human mitochondrial ferritin, sulfur oxygenase reductase and small heat-shock protein) are compared top-to-bottom. The starting points are polyhedra with octahedral symmetry 432 enclosing the cage and delimiting the central cavity, respectively, which have vertices at points of a species-dependent cubic form lattice. The approach is extended from the whole cage to axial-symmetric clusters down to polyhedral forms of single monomers viewed along the fourfold, the threefold and the twofold axes, respectively. The corresponding projected monomeric forms can be approximated by two-dimensional tiles, 13 enantiomorphic pairs in total. The determination of the cubic indices of the monomeric vertices opens the possibility of the way back analysis, bottom-to-top, as discussed in paper II [Janner (2008). Acta Cryst. A64, 503-512].

In paper I [Janner (2008). Acta Cryst. A64, 494-502], the enclosing forms of the monomers of four octahedral holoenzymes (bacterio and mitochondrial ferritins, small heat-shock protein and sulfur oxygenase reductase) were derived, with vertices at points of a cubic lattice and indexed accordingly. The correspondence between vertices and neighboring residues allows a sequential ordering of the vertices within the polyline defined by the C(alpha) atoms of the primary structure. The alignment of these sequences shows that the form vertices denoted as turning points delimit the elements of the secondary structure (alpha-helices, beta-strands and loops). This relation is analyzed further in a plot of angular changes in orientations of the polyline segments and planes as a function of the residue numbers and of the form vertices, respectively, leading to an alternative characterization of the ternary structure. Finally, two simple connectivity models of monomers, oriented according to the symmetry axes of the octahedral point group 432, suggest possible patterns in the self-assembly process from clusters of monomers to the quaternary structure of the cubic cage.