A New Model of Hemoglobin Oxygenation

Abstract

The study of hemoglobin oxygenation, starting from the classical works of Hill, has laid the foundation for molecular biophysics. The cooperative nature of oxygen binding to hemoglobin has been variously described in different models. In the Adair model, which better fits the experimental data, the constants of oxygen binding at various stages differ. However, the physical meaning of the parameters in this model remains unclear. In this work, we applied Hill's approach, extending its interpretation; we obtained a good agreement between the theory and the experiment. The equation in which the Hill coefficient is modulated by the Lorentz distribution for oxygen partial pressure approximates the experimental data better than not only the classical Hill equation, but also the Adair equation.

Keywords: Hill coefficient; Hill equation; allosteric interactions; cooperative binding of ligands; oxyhemoglobin dissociation curve.

Figure 1

Phenomenological model of oligomer liganding. I, initial (unliganded) state of oligomer; II/a–d, liganding steps (hemoglobin oxygenation); III, terminal state (complete liganding). Digits indicate: 1, ligand; 2, resultant interaction of oligomer with ligand; 3, oligomer; 4, interaction component of the liganded subunit; 5, interaction component of the conjugated subunit; 6, mediated interaction component through the conjugated subunit. Color of arrows and subunits denotes from inhibition (warm) to promotion (cold) of oxygenation.

Figure 2

Experimental data points of the hemoglobin dissociation curve: 1, according to Winslow et al. [27] and 2, according to Severinghaus [28].

Figure 3

Approximation of the experimental oxygenation curve, represented in logarithmic coordinates, by the classical Hill equation: (a) from the data set of Winslow et al. [27] and (b) from the data set of Severinghaus [28]. Legend: 1, experimental data points; 2, approximation; 3 and 4, upper and lower bounds of the confidence intervals, respectively; 5 and 6, upper and lower bounds of the prediction intervals, respectively. For all types of intervals, the confidence probability was 0.9999.

Figure 4

Approximation of the experimental oxygenation curve, represented in logarithmic coordinates, by the Adair equation: (a) from the data set of Winslow et al. [27] and (b) from the data set of Severinghaus [28]. Legend: 1, experimental data points; 2, approximation; 3 and 4, upper and lower bounds of the confidence intervals, respectively; 5 and 6, upper and lower bounds of the prediction intervals, respectively. For all types of intervals, the confidence probability was 0.9999.

Figure 5

Approximation of the experimental oxygenation curve, represented in logarithmic coordinates, by the Hill equation with h modulated by the Gauss distribution: (a) from the data set of Winslow et al. [27] and (b) from the data set of Severinghaus [28]. Legend: 1, experimental data points; 2, approximation; 3 and 4, upper and lower bounds of the confidence intervals, respectively; 5 and 6, upper and lower bounds of the prediction intervals, respectively. For all types of intervals, the confidence probability was 0.9999.

Figure 6

Approximation of the experimental oxygenation curve, represented in logarithmic coordinates, by the Hill equation with h modulated by the Lorentz distribution: (a) from the data set of Winslow et al. [27] and (b) from the data set of Severinghaus [28]. Legend: 1, experimental data points; 2, approximation; 3 and 4, upper and lower bounds of the confidence intervals, respectively; 5 and 6, upper and lower bounds of the prediction intervals, respectively. For all types of intervals, the confidence probability was 0.9999.