Theoretical Simulation of Red Cell Sickling Upon Deoxygenation Based on the Physical Chemistry of Sickle Hemoglobin Fiber Formation

The polymerization of the mutant hemoglobin S upon deoxygenation to form fibers in red blood cells of patients suffering from sickle-cell anemia results in changes in cell shape and rigidity, also known as sickling, which underlie the pathology of the disease. While much has been learned about the fundamental physical chemistry of the polymerization process, transferring these insights to sickling of red cells under in vivo conditions requires being able to monitor, and ultimately predict, the time course of cellular sickling under physiological conditions of deoxygenation. To this end, we have developed an experimental technique for tracking the temporal evolution of the sickling of red blood cells under laboratory deoxygenation conditions, based on the automated analysis of sequences of microscope images and machine-learning analysis to characterize cell morphology. As an aid in the quantitative understanding of these experiments, we have developed a computational framework for simulating the time dependence of sickling in populations of red blood cells which incorporates the current theoretical and empirical understanding of the physical chemistry of the sickling process. In order to apply these techniques to our experiments, we have theoretically determined the time course of deoxygenation by solving the diffusion equation for oxygen in our experimental geometry. With this combined description, we are able to reproduce our experimentally observed kinetics of sickling, suggesting that our theoretical approach should be applicable to physiological deoxygenation scenarios.