A Mathematical Graph-Theoretic Model of Single Point Mutations Associated with Sickle Cell Anemia Disease

Many diseases like cystic fibrosis and sickle cell anemia disease (SCD), among others, arise from single point mutations in the respective proteins. How a single point mutation might lead to a global devastating consequence on a protein remains an intellectual mystery. SCD is a genetic blood-related disorder resulting from mutations in the beta chain of the human hemoglobin protein (simply, β-globin), subsequently affecting the entire human body. Higher mortality and morbidity rates have been reported for patients with SCD, especially in sub-Saharan Africa. Clinical management of SCD often requires specialized interdisciplinary clinicians. SCD presents a major global burden, hence an improved understanding of how single point mutations in β-globin results in different phenotypes of SCD might offer insight into protein engineering, with potential therapeutic intervention in view. By use of mathematical modeling, we built a hierarchical (nested) graph-theoretic model for the β-globin. Subsequently, we quantified the network of interacting amino acid residues, representing them as molecular system of three distinct stages (levels) of interactions. Using our nested graph model, we studied the effect of virtual single point mutations in β-globin that results in varying phenotypes of SCD, visualized by unsupervised machine learning algorithm, the dendrogram.