Strongly correlated structure of axial-symmetric proteins. I. Orthorhombic, tetragonal, trigonal and hexagonal symmetries.

The geometry of the molecular envelope and channel in axial-symmetric proteins is investigated in order to test the validity of rules deduced previously from several other biomacromolecules. Again, molecular forms with remarkable geometric properties are found. In particular, for order of rotation N = 2, 3, 4, 6 the molecular forms encapsulating the C(alpha) backbone of the protein have vertices at lattice points and therefore integral indices. These lattices are characterized by a height-to-width axial ratio that reduces the number of free parameters and enhances the symmetry.