## 2 Biphasic Autoxidation Curves Observed in Human HbO\({}_{2}\) in Acidic Solutions
The reaction process was followed in each experimental run by the ratio ([HbO\({}_{2}\)]/[HbO\({}_{2}\)]\({}_{0}\)) of HbO\({}_{2}\) concentration after time \(t\) to that at time \(t\) = 0 that was monitored by the absorbance ratio of (A\({}_{t}-\)A\({}_{\infty}\))/(A\({}_{0}-\)A\({}_{\infty}\)) at 576 nm (\(\alpha\)-peak of HbO\({}_{2}\)). The ratio was then plotted against time. Each curve shown in Figure 2 represents the \(\rm-ln([HbO_{2}]/[HbO_{2}]_{0})\)_versus_ time plot (first-order plot) for this phenomenon. In acidic solutions (Figure 2(a)), the reaction was biphasic and can be described by first-order kinetics containing two rate constants as follows:  
\[\rm d[HbO_{2}]/dt=P\cdot exp(-\textit{k}_{\rm A}^{f}\cdot t)+(1-P)\cdot exp(- \textit{k}_{\rm A}^{s}\cdot t) \tag{2}\]  
Figure 1: Spectral changes over time from 450 nm to 650 nm following human HbO\({}_{2}\) autoxidation, redrawn from [PERSON] _et al_. [16]. The changes were monitored in 0.1 M 2-(\(N\)-morpholino) ethanesulfonic acid monohydrate (MES) buffer (pH 5.3) at 37 \({}^{\circ}\)C. Conditions: HbO\({}_{2}\) concentration was 125 \(\upmu\)M (in heme contents); the scanning interval was 30 min. This equation was originally proposed by [PERSON] and [PERSON] [14], where \(k_{\Lambda}\)\({}^{f}\) and \(k_{\Lambda}\)\({}^{s}\) represent first-order rate constants for the initial fast oxidation and the second slower oxidation, respectively, and \(P\) is the molar fraction of the initial fast component. In Figure 2(a), solid lines represent the best fitting derived by the least-squares method using the equation to each run. However, as shown in Figure 2(b), when the pH of solutions is \(>\)8, a plot of -ln([HbO\({}_{2}\)]/[HbO\({}_{2}\)]\({}_{0}\)) _versus_ time showed a single-phase reaction with a single first-order rate constant, although curve fittings could be made using the same equation under conditions of \(P=0.5\) and \(k_{\Lambda}\)\({}^{f}=k_{\Lambda}\)\({}^{s}\). Thus, it was shown that the biphasic behavior seen in acidic solutions gradually disappeared with increasing pH of solutions and completely disappeared if the pH of solutions was \(>\)8. In this way, the kinetic parameters and molar fraction of the initial fast component (\(P\)) for the biphasic nature of human HbO\({}_{2}\) autoxidation were established in each run in 0.1 M buffer at 37 \({}^{\circ}\)C (Table 1). It was evident that the values of \(P\) varied from 0.47 to 0.53. This means that HbO\({}_{2}\) was autoxidized with half of the component via the reaction process with the initial fast reaction with \(k_{\Lambda}\)\({}^{f}\) and the other half via the procedure with the second slower rate (\(k_{\Lambda}\)\({}^{s}\)). Thus, autoxidation of human HbO\({}_{2}\) may be written as follows:  
Figure 2: A –ln([HbO\({}_{2}\)]\({}_{0}\)/[HbO\({}_{2}\)]\({}_{0}\)) _versus_ time plot (first-order plot) for human HbO\({}_{2}\) autoxidation, redrawn from [PERSON] _et al_. [16]. (**a**) Acidic autoxidation seen in acidic-to-neutral pH ranges and (**b**) alkaline autoxidation in alkali solutions. Solid lines represent the least-squares fitting to experimental data in each run. Conditions: HbO\({}_{2}\) concentration was 50–125 \(\upmu\)M (in heme contents); and the reaction proceeded in 0.1 M buffer at 37 \({}^{\circ}\)C.  
(2)  
To clarify the processes behind this phenomenon, the obtained values of \(k_{\mathrm{A}}{}^{s}\)/\(k_{\mathrm{A}}{}^{f}\) were plotted against the pH of solutions (Figure 3).