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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 [Xm(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 [Xm(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 [Xm(ESRc)] at Rc = Xm(Rc) were evaluated using the linear functions of the negative standard free energy gap with Rc. The values of Xm(ESRc) were mostly in very good agreement with the values of Xm(ES). This implies that the energy gap law and the extend Dutton law are equivalent. Xm(ES) values in ET donors displaying the linear extend Dutton law with Rc were obtained by energy gap law, and then Xm(Rc) values were evaluated with the negative standard free energy gap. Thus, the obtained Xm(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.

The mechanism of photoinduced electron transfer (ET) from benzoate (Bz) and aromatic amino acids to the excited isoalloxazine (Iso*) in the D-amino acid oxidase–benzoate complex (DAOB) dimer from porcine kidney was studied using molecular dynamics simulation (MDS) and an electron transfer theory, and compared with that in the DAOB monomer. The DAOB dimer displayed two fluorescent lifetime components of 0.85 ps and 4.8 ps, as reported. The ET parameters contained in the Kakitani and Mataga (KM) model were determined so as to reproduce these lifetimes with MDS atomic coordinates. The Bz–isoalloxazine (Iso) distances were 0.66 nm in subunit A (Sub A), 0.68 nm in subunit B (Sub B) and 0.61 nm in the monomer. The fluorescent lifetimes of 4.8 ps and 0.85 ps were found to originate from Sub A and Sub B, respectively. In Sub A, Tyr228 was the fastest ET donor followed by Bz and Tyr55, while Bz was followed by Tyr228 and Tyr314 in Sub B. The ET rate from Bz was fastest in Sub B, followed by that in Sub A and the DAOB monomer. The static dielectric constants obtained near Iso were 2.4–2.6 in the DAOB dimer and monomer and 5.8–5.9 in holo D-amino oxidase (DAAO). The different dielectric constants could account for the experimental fluorescence peak observed for DAOB (524 nm) and DAAO (530 nm). Logarithmic ET rates decreased linearly with the donor–acceptor distance expressed by both center to center distance (Rc) and edge to edge distance (Re) in Sub A and Sub B of DAOB dimer and monomer, which reveals that the conventional Dutton rule holds in the ET processes in DAOB. The logarithmic ET rates were decomposed into the electronic coupling (EC), square root (SQ) and exponential (GTRAM) terms. It was found that both the EC term and the GTRAM term also decreased linearly with Rc. The sum of the slopes in the EC and GTRAM vs. Rc plots coincided with the slopes in the logarithmic ET rate vs. Rc functions, suggesting that the GTRAM term makes a significant contribution to the linear relations between logarithmic ET rate and Rc.

We have investigated primary processes of ultrafast photoreactions of various photoresponsive proteins by means of fs fluorescence dynamics measurements. Based on these studies, the effects of the protein nanospace (PNS), containing the chromophore, on the dynamics and mechanisms of the ultrafast and highly efficient reactions of these proteins have been elucidated. In this article, we discuss mainly the results of our studies on ultrafast photoisomerization of photoactive yellow protein (PYP), its mutants and analogues. The chromophore of the PYP, deprotonated coumaric acid thioester (O−-phenyl-CHCH–CO–S–CH2–), fixed in PNS by hydrogen (H) bonding interactions at the head part, O−-phenyl-, and by covalent bonding at the tail part, –CO–S–, undergoes ultrafast twisting by flipping the thioester bond, owing to the intrachromophore head to tail charge transfer caused by the photoexcitation. In the site-directed mutants where the PNS structure is looser and more disordered, the photoinduced twisting reaction becomes slowed compared with the wild-type PYP and moreover, the twisting becomes much slower in the denatured PYP, showing the supreme importance of more regulated PNS for the fast twisting. We found also coherent vibrations in the fluorescence decay curves which might be coupled with the twisting. Furthermore, we found for a PYP analogue with replaced chromophore ultrafast dynamic Stokes shift of fluorescence rather than the quenching due to twisting, indicating the importance of chromophore-PNS fine adjustment for the ultrafast twisting.

Electron-transfer reactions in an H-bonded assembly composed of a diacylaminopyridine bearing zinc porphyrin and 1,8:4,5-naphthalenetetracarboxylic diimide (Ka = 2.8 × 102 dm3 mol–1) in benzene occur with kCS = 4.1 × 1010 s–1 and kCR = 3.7 × 109 s–1, while the corresponding covalently linked model with a comparable distance and energy gap undergoes electron transfer with kCS = 9.9 × 1010 s–1 and kCR = 6.7 × 108 s–1.