Fitting Parameters of a Modified Hill’s Equation and Their Influence on the Shape of the Model Hemoglobin Oxygenation Curve

Abstract

Oxygen binds to hemoglobin cooperatively, and a correct description of this binding is relevant not only for understanding the mechanisms of involved molecular processes but also for clinical purposes. Hill’s equation, derived over a hundred years ago, is still the simplest and most efficient way to perform this description. However, in terms of accuracy, it is inferior to Adair´s equation, which contains more parameters. We proposed to use a modified Hill equation and showed that it allows a more accurate description of the binding of oxygen to hemoglobin than Adair’s equation. At the same time, unlike Adair’s equation, our model retains the physical meaning given to the original Hill equation. We considered and analyzed the influence of the equation parameters on the course of the oxygenation curve and presented the relationship between the fitting parameters and other parameters derived from them in the form of a diagram-graph, which, in our opinion, simplifies the perception of these estimates and can be useful in solving a number of problems for which the traditional way of analyzing the degree of cooperative interaction was via the Hill equation. We suggest that the newly proposed parameter hmax introduced in our model should be regarded as crucial for a better description of the oxygenation curve.

Keywords

• cooperativity
• oxygenation
• oxygenation curve
• oxyhemoglobin dissociation curve
• Hill equation
• Hill coefficient