## 2 Biphasic Autoxidation Curves Observed in Human HbO\({}_{2}\) in Acidic Solutions  
In this section, we focus on the biphasic nature of the autoxidation of human HbO\({}_{2}\) seen in acidic solutions. The phenomenon can be described by first-order kinetics containing two rate constants, \(k_{A}{}^{f}\) for the initial fast oxidation and \(k_{A}{}^{s}\) for the second slower oxidation, respectively, on the basis of our previous report [16]. This issue was the starting point that led us to uncover a new function of the \(\alpha_{1}\)-\(\beta_{1}\) (and \(\alpha_{2}\)-\(\beta_{2}\)) contact existing in the Hb molecule. HbO\({}_{2}\) was prepared from freshly drawn samples of human blood (total, 50-80 mL) obtained from healthy donors. Samples were centrifuged at 2,400 \(\times\)\(g\) for 10 min to remove supernatant plasma and buffy coats. The erythrocytes obtained were washed five times with ice-cooled 0.9% NaCl solution (saline) by centrifugation and hemolyzed by adding the same volume of ice-cooled distilled water. The hemolyseate was then fractionated with ammonium sulfate between 20% saturation and 70% saturation at pH 6.8. After dialysis, this solution was passed through two Sephadex G-50 columns (5 \(\times\) 90 cm) equilibrated with 10 mM Tris-HCl (pH 8.6). The effluent Hb fraction was further separated using a diethylaminoethyl (DEAE)-cellulose column (3 \(\times\) 15 cm) equilibrated with 10 mM Tris-HCl (pH 8.6) and washed sequentially with stepwise changing of buffer solutions as follows: (i) 60 mM Tris-HCl (pH 8.0); (ii) 100 mM Tris-HCl (pH 7.5); finally (iii) 100 mM NaCl with 100 mM Tris-HCl (pH 8.0). HbO\({}_{2}\) (human adult) was eluted out as the major fraction with 60 mM Tris-HCl (pH 8.0) and used in the experiments after dialyzing against 5 mM Tris-HCl buffer (pH 8.5). The autoxidation reaction was measured by UV/VIS spectroscopic means in 0.1 M buffer over a wide pH range (5.3-10.5) at 37 \({}^{\circ}\)C. Two milliliters of solution containing 0.2 M buffer was placed in a test tube and incubated in a waterbath maintained at 37 \(\pm\) 0.1 \({}^{\circ}\)C using a NESLAB temperature control system (Model RTE-100 or 111 or 210; NESLAB Instruments, Inc., Portsmouth, NH, USA). The reaction was started by adding the same volume of fresh HbO\({}_{2}\) solution (50-125 \(\upmu\)M in heme contents). The reaction mixture was then quickly transferred to a spectrophotometric cell (Spectrocell, Type Inject-A-Cell; Funakoshi Co., Tokyo, Japan) with a screwcap stopper. Changes in absorption at 450-650 nm were recorded on the same chart at measured time intervals. Spectra were recorded using an UV/VIS spectrophotometer (JASCO, Model Ubest-50 or V-560 or V-570; Japan Spectroscopic Co., Tokyo, Japan), equipped with a thermostatically controlled (within \(\pm\)0.1 \({}^{\circ}\)C) cell holder. At the final state of each run, Hb molecules were all completely converted to the ferric met form by addition of potassium ferricyanide. The buffers used were: acetate for pH 4.5-5.5, 2-(\(N\)-morpholino) ethanesulfonic acid monohydrate (MES) for pH 5.0-6.75, \(N\)-2-hydroxylpiperazine-\(N^{\prime}\)-2-ethanesulfonic acid (HEPES) for pH 6.55-8.3, 2-(cyclohexylamino) ethanesulfonic acid for pH 8.2-10.2, and 3-cyclohexylaminopropanesulfonic acid for pH 10.0-10.5. Figure 1 shows an example of the spectrophotometric changes over time from 450 nm to 650 nm for autoxidation of human HbO\({}_{2}\) when observed in 0.1 M MES buffer (pH 5.3) at 37 \({}^{\circ}\)C. In this reaction process, HbO\({}_{2}\) was autoxidized to its ferric met form through the tendency of the bound O\({}_{2}\) to oxidize ferrous heme iron (II) with generation of superoxide anions (O\({}_{2}\)):  
\[k_{\rm A} \tag{1}\] \[\rm Hb(II)O_{2}\rightarrow\rm metHb(III)+4(O_{2}^{-})\]  
Here \(k_{\rm A}\) represents the observed rate constant of the reaction at a given pH and temperature.