Electron equilibration

QM/MM approaches where the solute is QM and the solvent MM are in principle useful for computing the effect of the slow reaction field (represented by the solute point charges) but require a polarizable solvent model if electronic equilibration to the excited state is to be included (Gao 1994). With an MM solvent shell, it is no more possible to compute differential dispersion effects directly than for a continuum model. An option is to make the first solvent shell QM too, but computational costs for MC or MD simulations quickly expand with such a model. Large QM simulations with explicit solvent have appeared using the fast semiempirical INDO/S model to evaluate solvatochromic effects, and the results have been promising (Coutinho, Canute, and Zemer 1997 Coutinho and Canute 2003). Such simulations offer the potential to model solvent broadening accurately, since they can compute absorptions for an ensemble of solvent configurations. 

Adiabatic process (quantum mechanics) — In quantum mechanics a process is called adiabatic if electrons equilibrate with nuclei as they move. The concept of quantum adiabaticity was introduced by Paul Ehrenfest (1880-1933) as early as 1917, using pre-Heisenberg quantum mechanics [i]. The idea survived the advent of post-Heisenberg quantum mechanics, and was brought into its modern form by -> Born [ii]. The existence of adiabatic processes is readily proved by considering... 

Flash photolysis of the mixed-valence cytochrome oxidase-CO compound leads to a drop in the apparent reduction potential of cytochrome ay, and this results in a backflow of electrons from cytochrome a to the other redox sites. Three kinetic phases can be observed [26, 41], with relaxation rate constants (i.e., the sum of the rate constants for the forward and reverse reactions of the equilibria involved) of 3 X 10, 2 X 10, and 10 s . The first two phases involve ET fl3 —> a and a Cua, respectively the third phase is strongly pH-dependent and represents further electron re-equilibration between a-i and a, following the dissociation of a proton caused by the initial oxidation of a-i [26, 41a], as will be further discussed in Section 3.4.4. Direct electron equilibration between ai and Cua is not observed. 

The conversion P F (Figure 7) is accompanied by an electron equilibration between Cua and cytochrome a, and its rate is pH-dependent [60] and displays a kinetic isotope effect in D2O [60b]. Consequently, it has been suggested [51, 60a,c] that the formation of F is controlled by the protonation of the binuclear site. The conclusion that F really is a ferryl ion intermediate is supported by resonance-Raman measurements [61]. 

Electrons from cytochrome c are transferred rapidly (k = 8xl0 M -s ) to haem a and Cu - Although the former has been suggested to be the primary electron acceptor, this view is presently uncertain due to the very fast electron equilibration between the two receiving centres [127,128],... 

Electron transfer per se from haem a to the binuclear site, over a distance of ca. 7-9 A between the edges of the two haem groups, is expected to be very fast (t = a few nanoseconds) . Although haem-haem electron transfer with a time constant of ca. 3 ps has been measured in several laboratories, there are indications of a much faster rate of electron tunneling (but see also ref. 30). Yet, the electron transfer rate measured is already about three orders of magnitude faster than E ax, and can hence hardly be the cause of the limitation in the resting enzyme. However, the observed 3 ps electron transfer is an electron equilibration between haems r/j and a after reduction of haem as in the presence of CO, followed by flash photolysis of CO. 

The CO2 radicals react with disulfide groups in hCp at diffusion controlled rates to produce the RSSR radicals monitored at 410 nm (where RSSR radicals exhibit an absorption maximum) while no direct reduction of TlCu was observed (72). Instead, the electrons were further transferred to a Tl(Cu ) center in an intramolecular process with a rate constant of 28 2s at 279 K. An mframolecular electron equilibration with the T2/T3 center was then observed with a rate constant of 2.9 0.6 s determined independently at both 610 nm (TlCu absorption maximum) and at 330 nm, where the oxidation state of the trinuclear center can be monitored independently [Fig. 11 (a and fc)]. The internal ET process... 

The equihbrium constant of 3.4 0.5 at 25°C, pH 7.0 for the rapid electron equilibration step (Eq. 24) in bovine COX (49) corresponds to a difference in reduction potentials between the heme-a [Fe /Fe°] and Cua [Cu /Cu ] couples of 31 4 mV, which differs from earlier values, where an eP = 276 mV was reported for heme-a and 288 mV for Cua, that is, a difference of 12mV (154). The discrepancy is not surprising, however, considering the disparate experimental conditions employed in the earlier studies O.IM phosphate buffer saturated with 1 atm CO, which maintains heme a3-CuB in the reduced state. The observed equilibrium constant of 3.4 is in good agreement with results obtained by Kobayashi et al. (151) (X 1—4) and by Einarsdottir and co-workers (K = 2) (155). In experiments where a binuclear polypyridine ruthenium(ll) complex (bound electrostaticaUy to cytochrome oxidase) was... 

Similar PR experiments performed on P. denitrificans COX (50) have also revealed a rapid CuA-heme-a electron equilibration step with an observed rate constant of 30,430 2,300 s and with an equilibrium constant of 2.0 0.1 at 25°C, pH 7.0 (cf. Table VII) corresponding to a difference in reduction potentials between the heme-a [Fe /Fe )] and Cua [Cu VCu ] couples of + 18 + 1 mV. For Cua in this enzyme, a midpoint potential of 213 mV versus SHE was found under the aforementioned conditions (157), while the potential of heme-a was reported to be 428 mV versus SHE (158). The observed equilibrium constant thus disagrees considerably with an equilibrium constant calculated from these potential differences (K = 4300). This is not surprising. 

Figure 25. Reaction scheme for the proposed internal electron equilibration between the different redox centers in xanthine oxidase. [Adapted from Ref. (167)].

As summarized earlier, there is consensus with regard to the sequence of electron transfer in cytochrome oxidase. The Cua center is the initial acceptor of electrons from cytochrome c (k 3 x 10 M s ). This electron transfer depends crucially on a conserved tryptophan residue in subunit II ca. 5 A away from the Cua center. Then follows fast electron equilibration between Cua and the low-spin heme (kf 10 s kr 5 x 10 s, kf and kr denoting the... 

The nature of the dark recovery from DBMIB inhibition is not known, but a decreased binding to reduced cytochrome f or FeS seems unlikely in that the rate of cytochrome f rereduction in the dark was much faster than that of recovery from inhibition (Fig. 3). I have previously suggested that the bound form of DBMIB in the inhibited complex is the semiquinone or quinone form [9]. Recovery may involve slow reduction of these to the noninhibitory quinol form under these conditions. Regardless of this problem, however, it seems likely that the bf complex is functionally monomeric from these data, although the reason for discrepancy with previous data is not clear. It was found in these experiments that progressive inhibition with DBMIB took the form of a decreased rate constant for reduction of all of the cytochrome f, rather than an inhibition of a fraction of the population. This effect has already been noted by Jones and Whitmarsh [10] who interpreted it in terms of rapid exchange of DBMIB between bf complexes. The present work shows that this is not possible and instead the effect must arise from rapid (< 1ms) electronic equilibration between the high potential centres of the bf complexes caused by plastocyanin. 

A so-called electron equilibration method (EEM), finally, is used to calculate the atomic charges in a consistent manner." " ... 

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