A finite Hopfield neural network model for the oxygenation of hemoglobin
Juan Miguel Castellanos-Jaramillo, Arnulfo Castellanos-Moreno, Adalberto Corella-Madueño · Physica Scripta · 2020
Abstract A model of the oxygenation of hemoglobin is developed based in a finite Hopfield neural network. The model is based in two transition probabilities, w + and w − , between the states + 1 , − 1 of each neuron. The oxygen partial pressure, PO 2 , is introduced by an external field h ; and the cooperativity phenomenon appears as a field h r , this includes the interaction between the four binding sites of the hemoglobin. The results of oxygen saturation as a function of PO 2 present a sigmoidal curve, similar to oxygen-hemoglobin saturation curves (ODCs) from Severinghaus. These simulated ODCs present properties that are compatible with those from ODCs that are studied in medical practice and scientific research. The curves obtained shift to the left if cooperativity increases, and shift to the right if cooperativity decreases. Other parameters that are obtained are: the Hill coefficient, n H ; the PO 2 at half saturation, P 50 ; the maximum saturation when PO 2 reaches 100 torr; θ max , and the equilibrium constant k = k D − 1 .