A local spin model to describe the magnetic interactions in biological molecules containing [4Fe-4S](+) clusters, application to Ni-Fe hydrogenases

Structural information on the relative arrangement of paramagnetic centers can be obtained through the quantitative study of their magnetic interactions based on the numerical simulation of EPR spectra recorded at different microwave frequencies. In a recent work, we have shown that such studies must explicitly take into account the delocalization of the magnetic moments over polynuclear clusters, and we have presented a local spin model suited for valence-localized clusters (Bertrand, P.; More, C.; Guigliarelli, B.; Fournel, A.; Bennet, B,; Howes, B. J. Am. Chern. Sec. 1994, 116, 3078-3086). In this paper, we examine the more general situation in which the cluster contains partially or completely delocalized mixed-valence pairs. This situation is encountered in particular in the case of [4Fe-4S] clusters which are ubiquitous in biological systems. A model is presented and developed for a system containing a [4Fe-4S](+) cluster magnetically coupled to a mononuclear center. This model is then applied to the study of the magnetic interactions between the nickel center and the proximal [4Fe-4S](+) cluster in the active form of Desulfovibrio gigas hydrogenase. The arrangement at atomic resolution deduced from this study is compared to that given by a recent X-ray crystal study carried out on the inactive form of the same enzyme.