Spin-lattice relaxation of coupled metal-radical spin-dimers in proteins: application to Fe(2+)-cofactor (Q(A)(-.), Q(B)(-.), phi(-.)) dimers in reaction centers from photosynthetic bacteria

The spin-lattice relaxation times (T(1)) for the reduced quinone acceptors Q(A)(-.) and Q(B)(-.), and the intermediate pheophytin acceptor phi(-.), were measured in native photosynthetic reaction centers (RC) containing a high spin Fe(2+) (S = 2) and in RCs in which Fe(2+) was replaced by diamagnetic Zn(2+). From these data, the contribution of the Fe(2+) to the spin-lattice relaxation of the cofactors was determined. To relate the spin-lattice relaxation rate to the spin-spin interaction between the Fe(2+) and the cofactors, we developed a spin-dimer model that takes into account the zero field splitting and the rhombicity of the Fe(2+) ion. The relaxation mechanism of the spin-dimer involves a two-phonon process that couples the fast relaxing Fe(2+) spin to the cofactor spin. The process is analogous to the one proposed by R. Orbach (Proc. R. Soc. A. (Lond.). 264:458-484) for rare earth ions. The spin-spin interactions are, in general, composed of exchange and dipolar contributions. For the spin dimers studied in this work the exchange interaction, J(o), is predominant. The values of J(o) for Q(A)(-.)Fe(2+), Q(B)(-.)Fe(2+), and phi(-.)Fe(2+) were determined to be (in kelvin) -0.58, -0.92, and -1.3 x 10(-3), respectively. The |J(o)| of the various cofactors (obtained in this work and those of others) could be fitted with the relation exp(-beta(J)d), where d is the distance between cofactor spins and beta(J) had a value of (0.66-0.86) A(-1). The relation between J(o) and the matrix element |V(ij)|(2) involved in electron transfer rates is discussed.