Symmetry types, systems and their multiplicity in the structure of adenovirus capsid. I. Symmetry networks and general symmetry motifs.

Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino-acids--are in symmetrical location. Every kind of polypeptide forms a separately also symmetrical network in the capsid distributed according to their functions in the inner and outer side and the inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four (GOF) according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each GOF orient toward the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the GOFs: the hexons surround either a polypeptide IX or a polypeptide IlIa. The two versions of GOFs on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the antisymmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an antisymmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest neighbouring facets. In the facets, the polypeptide subunits of polypeptide IX centered GOF hexons have identical counter-clockwise orientation but the orientation of the neighbouring facets is always opposite compared to each other. On the five-fold symmetry axis, any facet can be "turned on" to the adjacent facet or "rotated" to all the others and will take the symmetry and orientation of the facet it got turned on or rotated to. Thus, every facet together with the polypeptides attached to it shows a twenty-fold symmetry and multiplicity. An other type of symmetry and multiplicity in the capsid is that perpendicular to the 6 five-fold rotation axes run a geodetic (equatorial) ribbon like motif (superfieces) altogether six made up of 10 x 10 triangular facets and bent ten-times with an angle of 36 degrees. A triangular facet participates in forming three ribbon-like motifs, which intersect with each other on the given facet, but the same three motifs intersect repeatedly only on the antisymmetrically located facet.