A multicomponent, random walk model of transport and metabolism inside a neuron

A model of multicomponent transport, consumption, and production of metabolites inside a neuron containing discrete mitochondria and glycolytic enzymes is developed using a random walk model of molecular transport. The ratio of anaerobic to aerobic metabolism which maximizes ATP production under normal, ischemic, and anoxic conditions is calculated. The ratio of the number of mitochondria to glycolytic enzymes which maximizes ATP under normal conditions is also calculated. Because the volume of the neuron is fixed, the sum of the number of mitochondria and glycolytic enzymes is fixed. This constraint is incorporated in the optimization process as an interior penalty function. Some of the advantages of employing the random walk technique are simple stoichiometry can be used to model consumption and production of metabolites, the geometry of the enzyme system and their active sites can be easily included in the model, and saturation of enzymes can be more easily modeled.