Equivalence between inverted regions of the energy gap law and inverted regions of donor–acceptor distances in photoinduced electron transfer processes in flavoproteins

In the present work, we discuss about the relationship between the energy gap law and extended Dutton law in flavoproteins. The extend Dutton law is defined herein as the dependence of logarithmic rates (ln Rate) of photoinduced electron transfer (ET) from aromatic amino acids to excited isoalloxazine (Iso*) on donor–acceptor distances (Rcs). Both functions of ln Rate vs. negative values of the standard free energy gap and ln Rate vs. Rc display a parabolic behavior, when the ET rates are ultrafast. The negative values of the standard free energy gap at peaks of ln Rate [X(m)(ES)] were obtained for FMN-binding protein, wild-type pyranose 2-oxidase, T169S (Thr169 is replaced by Ser) pyranose 2-oxidase, and medium-chain acyl-CoA dehydrogenase. The values of Rc at peaks of ln Rate [X(m)(Rc)] were also obtained for these flavoproteins. The negative values of the standard free energy gap decreased with approximate linear functions of Rc. The negative values of standard free energy gap [X(m)(ESRc)] at Rc = X(m)(Rc) were evaluated using the linear functions of the negative standard free energy gap with Rc. The values of X(m)(ESRc) were mostly in very good agreement with the values of X(m)(ES). This implies that the energy gap law and the extend Dutton law are equivalent. X(m)(ES) values in ET donors displaying the linear extend Dutton law with Rc were obtained by energy gap law, and then X(m)(Rc) values were evaluated with the negative standard free energy gap. Thus, the obtained X(m)(Rc) values were much smaller than the Rc range obtained by the method of molecular dynamics simulation. This suggests that ET processes with linear profiles of the extend Dutton law could be parabolic when Rc becomes much shorter than the Rc range obtained by the method of molecular dynamics simulation.