The Mathematical Model of Disturbance of Energy Metabolism in Brain during Development of Neurodegenerative Diseases: A Proposed Mechanism of Cell Death

The paper presents a theoretical study of the failure of energy metabolism in nervous tissue on a detailed biophysical model of metabolic coupling between neurons and astrocytes under afferent stimulation simulating by the release of glutamate into the presynaptic cleft. The main result of the model study is the detection of the phenomenon of adenylate collapse, the essence of which is the irreversible drop of ATP concentration after reaching the critical threshold value. This effect occurs as a result of the reversing of the reaction catalyzed by adenylate kinase. At high ATP values, the reaction equilibrium is shifted towards the formation of ADP from ATP and AMP. When the threshold is reached, the equilibrium shifts in the opposite direction, i.e., the formation of AMP and ATP from ADP occurs. If this situation is accompanied by a high consumption of ATP, the entire pool of adenine nucleotides goes into AMP. However, AMP is not phosphorylated, unlike ADP in glycolysis and oxidative phosphorylation, so the system quickly comes to depletion of ATP. Thus, adenylate collapse can be a new mechanism of the selective cell death in the development of neurodegenerative diseases.