Metalloprotein Electron Transfer. Cytochrome aa₃ Reduction Kinetics and Theoretical Formulation of Distance Dependence

The kinetics of anaerobic reduction of beef heart mitochondrial cytochrome c oxidase (cytochrome aa3) by hexammine ruthenium(II) (RuA62+) were measured. At wavelengths in the Soret and at 605 nm the kinetics are biphasic, neither phase exhibiting (pseudo-)first order behavior. A complete nonlinear optimization analysis showed that the slow phase obeyed strict second order kinetics, the fast phase being apparently more complex. Kinetic difference spectra observed for the RuA62+ reduction of native and cyanide-treated enzyme clearly demonstrate that the fast phase is due to reduction of cytochrome a3+ while the slow phase is due to reduction of a33+. The slow phase is independent of RuA62+ concentration with a second order rate constant of (1.04 ± .06) x 105 M-1-s-1 (25°C) and activation parameters △H≠ = 16.6 ± 0.6 kcal-mol-1, △S≠= +20.2 ± 2.0 cal-deg-1-mol-1 (pH = 6.0 (cacodylate), μ = 0.10 M) for native aa3. The oxidized-cyanide derivative gave a second order rate constant of (1.99 ± .06) x 104 M-1-s-1 (pH = 6.0 (cacodylate), μ = 0.10 M, 25°C). Analysis of the fast phase as a second order decay gave temperature-independent second order rate constants which are linearly dependent on RuA62+ concentration. The third order rate constant from this fit is (1.68 ± .02) x 1011 M-2-s-1 (pH = 6.0 (cacodylate), μ = 0.10 M, 25°C). The second order slow phase is interpreted as involving intermolecular electron transfer between half-reduced (cytochrome a reduced) species in reduction of cytochrome a3. A detailed description of the nonlinear least squares optimization techniques used for analysis of the cytochrome aa3 kinetics is given along with a general description of a complete kinetics analysis computer routine package. Emphasis is placed on correct error analysis and weighting procedures. In addition, a theoretical description of the dependence of the rate of metalloprotein electron transfer on the distance over which the transfer must occur is presented. The exponential dependence of rate on distance derived in several theoretical formulations of electron tunneling in biological systems is assumed and several known cases of metalloprotein electron transfer with small molecule reagents are examined to determine the distance of transfer. The results are compared with known structural data and discussed in terms of the accessibility of protein metal sites to external reagents.