Sphere Packing Screw Symmetry Koruga

There are 32 possible symmetry arrangements of packed spheres in a cylindrical crystal. Erickson (1973) used hexagonal packing of protein monomers to explain the form and patterns of viruses, flagella and microtubules. Djuro Koruga (1986) of the University of Belgrade's Molecular Machines Research Unit has analyzed the symmetry laws which describe cylindrical sphere packing and the structure of microtubules. Koruga has used both hexagonal packing and face centered cubic packing of spheres to explain microtubule organization. Koruga (1986):

The particular symmetry group which represents the packing of spheres in microtubules is 'Oh(6/4).' Hexagonal packing may be described by using fixed conditions if the centers of the spheres lie on the surface of the cylinder and if the sphere values in the long axis of the cylinder are the same as in the dimension of face centered cubic packing. The six fold symmetry and dimer configuration lead to screw symmetry on the cylinder: a domain may repeat by translocating it in a spiral fashion on the cylinder. From coding theory, the symmetry laws of tubulin subunits suggest that 13 protofilaments are optimal for the best known binary error correcting codes with 64 code words. Symmetry theory further suggests that a code must contain about 24 monomer subunits or 12 dimers.

Figure 8.6: Koruga's derivation of the symmetry of microtubules. With permission from Djuro Koruga (1986).

Koruga's symmetry arguments may be compared with the "gradion" concept of Roth, Pihlaja, and Shigenaka in which a field of about 17 monomers is thought to represent a basic information unit. Koruga also concludes that microtubule symmetry and structure are optimal for information processing.

2TIR = 2Tt

2TIR = 2Tt

Figure 8.7: Koruga's screw symmetry and optimal information unit in lattice wall of microtubule. With permission from Djuro Koruga (1986).

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