Abstract
The geometry proposition that "four points not in a plane describe one and only one sphere" provides a novel tool for analyzing protein-induced distortions in [4Fe-4S] clusters. A geometrically perfect reference structure comprises interlaced, regular tetrahedra of Fe, S, and Sγ atoms having T
d symmetry. Three circumspheres are defined by the three sets of four atoms, the circumcenters of which are unique points within the cluster. The structure is thus re-defined by the positions of the circumcenters in xyz space and the r, θ, φ of each atom on its respective sphere. Analysis of 12 high-resolution structures of protein-bound and small molecule [4Fe-4S](SR)4 clusters revealed: (a) the circumcenters are generally non-coincident by ~0.01 to ~0.06 Å; (b) the Fe radius, r
Fe, is nominally independent of core oxidation state, having values between 1.66 to 1.69 Å, whereas r
S and r
SG, which have ranges of 2.18–2.24 Å and 3.87–3.94 Å, respectively, both increase by as much as ~3% upon reduction from the 3+ to the 1+ core valence; (c) deviation of some atoms from the θ, φ of a perfect tetrahedron can be large, ~10°, and sets of atoms can show patterns of motion on their spheres that result from changes in Fe-S bond lengths. Density functional theory calculations suggest that the [4Fe-4S] core itself requires rather little energy to distort (~2 kcal/mol), whereas significantly more energy is required to distort the Sγ shell (~4 kcal/mol) to that of cluster I in Clostridium acidurici ferredoxin.