The architecture of the GroEL-GroES-(ADP)(7) chaperonin complex. I. Heptagrammal molecular forms

Molecular forms are considered with vertices that have integral coordinates (the indices) with respect to a symmetry-adapted basis and which are left invariant by a point group of crystallographic scale-rotations (represented in this basis by invertible integral matrices). The composite form enclosing the chaperonin complex GroEL-GroES-(ADP)(7) is derived and decomposed into heptagrammal forms. These are generalizations of the two-dimensional forms based on sevenfold star polygons. In the chaperonin complex, nine such heptagrammal molecular forms are found: three for each ring (trans and cis) of GroEL and three for GroES. These forms correspond to a splitting of the monomer into adjacent segments. The change in the folding of the chains in the cis ring of GroEL arising from binding to GroES leaves the chain segmentation invariant.