Principles of quasi-equivalence and Euclidean geometry govern the assembly of cubic and dodecahedral cores of pyruvate dehydrogenase complexes

The pyruvate dehydrogenase multienzyme complex (M(r) of 5–10 million) is assembled around a structural core formed of multiple copies of dihydrolipoyl acetyltransferase (E2p), which exhibits the shape of either a cube or a dodecahedron, depending on the source. The crystal structures of the 60-meric dihydrolipoyl acyltransferase cores of Bacillus stearothermophilus and Enterococcus faecalis pyruvate dehydrogenase complexes were determined and revealed a remarkably hollow dodecahedron with an outer diameter of ≈237 Å, 12 large openings of ≈52 Å diameter across the fivefold axes, and an inner cavity with a diameter of ≈118 Å. Comparison of cubic and dodecahedral E2p assemblies shows that combining the principles of quasi-equivalence formulated by Caspar and Klug [Caspar, D. L. & Klug, A. (1962) Cold Spring Harbor Symp. Quant. Biol. 27, 1–4] with strict Euclidean geometric considerations results in predictions of the major features of the E2p dodecahedron matching the observed features almost exactly.