Kinetic and Theoretical Comprehension of Diverse Rate Laws and Reactivity Gaps in <i>Coriolus hirsutus</i> Laccase-Catalyzed Oxidation of Acido and Cyclometalated Ru<sup>II</sup> Complexes

The reactivity of the acido Ru<sup>II</sup> complexes <i>cis</i>-[RuCl<sub>2</sub>(LL)<sub>2</sub>], [RuCO<sub>3</sub>(LL)<sub>2</sub>], <i>cis</i>-[RuCO<sub>3</sub>-(bquin)<sub>2</sub>] (LL = 2,2′-bipyridine (bpy) and 1,10-phenanthroline (phen); bquin = 2,2′-biquinoline) and cyclometalated Ru<sup>II</sup> derivatives of 2-phenylpyridine and 4-(2-tolyl)pyridine [Ru(<i>o</i>-C<sub>6</sub>H<sub>4</sub>-2-py)(phen)<sub>2</sub>]PF<sub>6</sub> (<b>1</b>), [Ru(<i>o</i>-C<sub>6</sub>H<sub>3</sub>-<i>p</i>-R-2-py)(bpy)(MeCN)<sub>2</sub>]PF<sub>6</sub> (<b>2</b>), and [Ru(<i>o</i>-C<sub>6</sub>H<sub>3</sub>-<i>p</i>-R-2-py)(phen)(MeCN)<sub>2</sub>]PF<sub>6</sub> (<b>3</b>) (R = H (<b>a</b>), Me (<b>b</b>)) toward laccase from <i>Coriolus hirsutus</i> has been investigated by conventional UV−vis spectroscopy at pH 3−7 and 25 °C. The acido and cyclometalated complexes are readily oxidized into the corresponding Ru<sup>III</sup> species, but the two types of complexes differ substantially in reactivity and obey different rate laws. The acido complexes are oxidized more slowly and the second-order kinetics, first-order in laccase and Ru<sup>II</sup>, holds with the rate constants around 5 × 10<sup>4</sup> M<sup>−1</sup> s<sup>−1</sup> at pH 4.5 and 25 °C. The cyclometalated complexes <b>1</b>−<b>3</b> react much faster and the hyperbolic Michaelis−Menten kinetics holds. However, it is <i>not</i> due to formation of an enzyme−substrate complex but rather because of the ping-pong mechanism of catalysis, viz. <i>E</i>(ox) + Ru<sup>II</sup> → <i>E</i>(red) + Ru<sup>III</sup> (<i>k</i><sub>1</sub>); <i>E</i>(red) + 1/4O<sub>2</sub> → <i>E</i>(ox) (<i>k</i><sub>2</sub>), with the rate constants <i>k</i><sub>1</sub> in the range (2−9) × 10<sup>7</sup> M<sup>−1</sup> s<sup>−1</sup> under the same conditions. The huge values of <i>k</i><sub>1</sub> move the enzymatic oxidation toward a kinetic regime when the dioxygen half-reaction becomes the rate-limiting step. Cyclometalated compounds <b>1</b>−<b>3</b> can therefore be used for routine estimation of <i>k</i><sub>2</sub>, that is, the rate constant for reoxidation for laccases by dioxygen. The mechanism proposed was confirmed by the direct stopped-flow measurements of the <i>k</i><sub>2</sub> rate constant (8.1 × 10<sup>5</sup> M<sup>−1</sup> s<sup>−1</sup> at 26 °C) and supported by the theoretical modeling of interaction between the bpy analogue of <b>1</b> and <i>Coriolus hirsutes</i> laccase using Monte Carlo simulations.