## 6 Mechanistic Details of Autoxidation of Human HbO\({}_{2}\): Computer Simulations
**(a)** The -ln([HbO\({}_{2}\)]/[HbO\({}_{2}\)]\({}_{0}\)) _versus_ time plot; **(b)** isoelectric-focusing electrophoretic profiles; and **(c)** polyacrylamide gel electrophoretic profiles. Solid lines represent the curves derived from the Runge–Kutta method with setting of the following constants: \(k_{\rm A}^{\,f}\) = 0.148 h\({}^{-1}\), \(k_{\rm A}^{\,s}\) = 0.0208 h\({}^{-1}\) and \(\Delta t\) = 0.1 h. For (b), the symbols are designated as follows: the 1 st (\(\circ\)), 2 nd (\(\Delta\)), 3 rd (\(\Delta\)) and 4 th peaks (\(\bullet\)), respectively. \(k_{\rm A}{{}^{f}}\)= 0.148 h\({}^{-1}\) (\(t_{1/2}\) = 4.7 h), \(k_{\rm A}{{}^{s}}\)= 0.0208 h\({}^{-1}\) (\(t_{1/2}\) = 1.4 d), and \(P\) = 0.51. Thus, by setting the values of \(k_{\rm A}{{}^{f}}\) and \(k_{\rm A}{{}^{s}}\) at 0.148 h\({}^{-1}\) and 0.0208 h\({}^{-1}\), respectively, and \(\Delta t\) = 0.1 h, the relevant concentration progress curves were displayed on a personal computer for the possible species assumed in this model. Figure 13 illustrates the outcomes: Figure 13(a) shows aspects of the spectrophotometric changes in terms of the -ln([HbO\({}_{2}\)]/[HbO\({}_{2}\)]\({}_{0}\)) _versus_ time plot, whereas Figure 13(b,c) describe aspects of the associated isoelectric-focusing electrophoretic profiles (Figure 13(b)) and polyacrylamide gel electrophoretic profiles (Figure 13(c)), respectively. In Figure 13, each computed curve (solid line) showed satisfactory-to-good agreements with the experimental data. These demonstrated that almost all of the reaction aspects could be fully explained by the consecutive changes of the species supposed in this model. Thus, the \(\beta\) chain was seen to carry delayed autoxidation in the tetrameric protein architecture. The rate of the initial rapid phase (\(k_{\rm A}{{}^{f}}\)) characterized with the HbO\({}_{2}\) autoxidation represented the intrinsic \(\alpha\)-chain oxidation, whereas the rate of the second slower phase (\(k_{\rm A}{{}^{s}}\)) reflected the intrinsic \(\beta\)-chain oxidation. These findings led us to conclude that the \(\beta\) chain manifests delayed autoxidation in the human HbO\({}_{2}\), which could be much more evident in acidic solutions. Innate Instability of the Hb Molecule, Its Degradation to Hemichrome, and Subsequent Formation of Heinz Bodies in Normal Human Erythrocytes during Mild Heating  
In this section, we discuss the results of our previous study investigating the formation of Heinz bodies in normal human erythrocytes [23,24]. Aliquots of freshly drawn venous blood from healthy donors were subjected to mild heating at \(>\)37 \({}^{\circ}\)C for 30 min to investigate hemichrome formation and subsequent Heinz-body formation in normal human erythrocytes. Heinz bodies were then visualized by exposing blood smears to acetylcholinesterasehydrazine and staining with crystal violet. Changes within the erythrocytes were observed using light microscopy under oil immersion. Prior to the acetylphenylhydrazine test [38,39], blood samples were subjected to mild heating _in vitro_. A 2-mL sample was placed in a test tube and incubated in a waterbath maintained at each desired temperature (\(\pm\)0.1 \({}^{\circ}\)C) above 37 \({}^{\circ}\)C for 30 min using a NESLAB temperature control system (Model RTE-100 or 111 or 210 or 221). In each experimental run, we employed a temperature-untreated reference as a control. The blood sample used as a temperature-untreated reference was kept at a low temperature (0-4 \({}^{\circ}\)C) for as long as possible after withdrawal from the donor, and never exposed to temperatures above room temperature. \(\beta\)-Acetylphenylhydrazine and crystal violet (research grade for pathology) were used (Wako Pure Chemical, Co., Osaka, Japan) for the procedure, as described by [PERSON] [39]. A 0.1-mL aliquot of blood sample was suspended in 2 mL of acetylcholinesterasehydrazine and 200 mg of glucose in 100 mL of 0.067 M phosphate buffer were dissolved at pH 7.6.