A mathematical analysis of cooperativity and fractional saturation of oxygen in hemoglobin

Authors : Roohi BHAT, Mukhtar Ahmad KHANDAY

Pages : 118-128

Doi:10.31801/cfsuasmas.1029614

View : 20 | Download : 12

Publication Date : 2023-03-30

Article Type : Research Paper

Abstract :Hemoglobin $insert ignore into journalissuearticles values(Hb);$ possesses good properties of cooperative system and it normally executes oxygen and other essential items via erythrocytes in the body. The chemical action of $Hb$ is to combine with oxygen  insert ignore into journalissuearticles values( O 2 ); insert ignore into journalissuearticles values(O2); in the lungs to form oxyhemoglobin insert ignore into journalissuearticles values( H b O 2 ); insert ignore into journalissuearticles values(HbO2); . Binding of oxygen with a hemoglobin is one of the important cooperative mechanism and is an emerging mathematical research area with wide range of applications in biomedical engineering and medical physiology. To this end, a mathematical model is proposed to study the fractional saturation of oxygen in hemoglobin to understand the binding effect and its stability at various stages. The mathematical formulation is based on the system of ordinary differential equations together with rate equations under different association and dissociation rate constants. The five states of the cooperative systems $Hb, HbO_2, Hbinsert ignore into journalissuearticles values(O_2);_2, Hbinsert ignore into journalissuearticles values(O_2);_3$ and $Hbinsert ignore into journalissuearticles values(O_2);_4$ are modelled and the Hill’s function has been used to approximate the binding effect and saturation of ligand $insert ignore into journalissuearticles values(O_2);$ with respect to various rate constants. Also, the Adair equation has been employed to interpret the saturation concentrations of oxygen in hemoglobin.
Keywords : Hemoglobin Hb, cooperativity, steady states, ordinary differential equations, rate equations, fractional saturation