Revealing the magnetostructural dynamics of [2Fe-2S] ferredoxins from reduced-dimensionality analysis of antiferromagnetic exchange coupling fluctuations.

Metalloproteins are biomolecular hybrids composed of an "inorganic core" embedded in a "bioorganic matrix". Cofactors typically contain transition metal clusters with complex electronic structure whereas the protein host undergoes dynamics on many length and time scales. This renders computational studies of spectroscopic properties challenging, in particular, when magnetic interactions are involved. In the present study we introduce a simplified description of the antiferromagnetic exchange coupling J in reduced dimensionality which allows one to study magnetostructural dynamics of [2Fe-2S] type iron-sulfur proteins in their oxidized form by molecular dynamics. It is demonstrated that parametrization in terms of a 2D J-surface faithfully reproduces the rigorous results both in vacuo and in Anabaena ferredoxin. In particular, we present a parametrization which relies on a spin-projected density functional approach based on two Kohn-Sham determinants corrected for self-interaction via a self-consistent linear-response Hubbard-U technique. This yields an average J for Anabaena Fd in close agreement with experimental in vitro results without any specific adjustment or fitting. The analytical J-surface can be used for [2Fe-2S] proteins in their oxidized form in general and the idea can be extended to other metalloproteins as well as to other spectroscopic properties.