The rationalization of carbon monoxide and hemoglobin association

Background/objective: Carbon monoxide (CO) is a colorless, odorless toxic gas responsible for approximately 100,000 emergency department visits and more than 420 deaths annually in the United States. Although CO–hemoglobin interactions have been extensively studied, a direct relationship between CO saturation and partial pressure has not been well established. This study aimed to derive a simple equation describing this relationship using principles analogous to the oxygen–hemoglobin association model. Methods: CO saturation was defined as the fraction of hemoglobin binding sites occupied by CO. Using chemical kinetics, the concentrations of CO, O₂, and hemoglobin, together with their association constants, were incorporated into the saturation formulation. Algebraic substitution and simplification yielded a rational function with four unknown coefficients. At a fixed oxygen partial pressure of 100 mmHg, four equilibrium (PCO, CO saturation) data points were used to solve for the coefficients of a fourth-degree rational function. Results: The derived CO–hemoglobin association equation reproduced the four derivation data points exactly and closely approximated additional literature values. The resulting association curve was hyperbolic. Fractional analysis demonstrated that Hb, HbCO, Hb(CO)₂, Hb(CO)₃, and Hb(CO)₄ fractions peaked at CO saturations of 0%, 25%, 50%, 75%, and 100%, respectively, with the triply bound form predominating overall. Conclusions: The CO–hemoglobin association could be described by a fourth-degree rational equation, enabling estimation of either CO saturation or CO partial pressure when one is known and providing a framework extendable to varying oxygen tensions.