A finite Hopfield neural network model for the oxygenation of hemoglobin

© 2020 IOP Publishing Ltd. 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, PO2 is introduced by an external field h; and the cooperativity phenomenon appears as a field hr this includes the interaction between the four binding sites of the hemoglobin. The results of oxygen saturation as a function of PO2 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, nH the PO2 at half saturation, P50; the maximum saturation when PO2 reaches 100 torr; θmax and the equilibrium constant k = kD-1 The Hill curve is satisfactorily fitted with the simulation data. Algebraic relation between nH, P50 and the cooperativity parameter J are also found; as well as a relation between θmax and J We establish a relation between the network temperature, T, and the temperature of the medium of the hemoglobin, Th measured in Celsius. It is found that when Th increases, nH, P50, θmax and k also increase. The change in pH, Δ pH, is found to be directly proportional to J; this means that alkaline mediums favor cooperative behavior. We also calculate the change in Gibbs free energy, Δ G, and notice that the values taken are negative and decrease as PO2 increases; this indicates that the oxygenation of hemoglobin is a spontaneous reaction. The change in enthalpy, Δ H, is also calculated for each value of J.