Mathematical Analysis of Molecular Hypotheses for Clinical Variation in Sickle Cell Disease

Abstract

Hemoglobin is the oxygen-binding protein in red blood cells. In sickle cell disease, a single point mutation in the gene that encodes a hemoglobin subunit causes the protein to polymerize at low oxygen tensions. Significant pathology, including vaso-occlusive crises, occurs when long polymers deform the cell into a sickle-like shape. Clinically, there exists substantial intra- and inter-disease type variation. However, limited experimental methods make it difficult, when not impossible, to test molecular hypotheses for this variation. Here, we extend an established mathematical model of sickle hemoglobin solubility to test new and old hypotheses. We suggest, contrary to past thinking, that different combinations of hemoglobin subunits can have different stabilities in solution, and we find that this variation can impact the amount of polymer formed in different scenarios. We also investigate how the single-cell distribution of fetal hemoglobin affects polymerization. We show that a common heuristic for determining which cells form polymer is only applicable in narrow circumstances, and we demonstrate how the mathematical model gives an alternative experimental route for determining the single-cell distribution of fetal hemoglobin.