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Configuration of the hemoglobin oxygen dissociation curve demystified: a basic mathematical proof for medical and biological sciences undergraduates.

The oxygen dissociation curve (ODC) of hemoglobin (Hb) has been widely studied and mathematically described for nearly a century. Numerous mathematical models have been designed to predict with ever-increasing accuracy the behavior of oxygen transport by Hb in differing conditions of pH, carbon dioxide, temperature, Hb levels, and 2,3-diphosphoglycerate concentrations that enable their applications in various clinical situations. The modeling techniques employed in many existing models are notably borrowed from advanced and highly sophisticated mathematics that are likely to surpass the comprehensibility of many medical and bioscience students due to the high level of "mathematical maturity" required. It is, however, a worthy teaching point in physiology lectures to illustrate in simple mathematics the fundamental reason for the crucial sigmoidal configuration of the ODC such that the medical and bioscience undergraduates can readily appreciate it, which is the objective of this basic dissertation.