Numerical simulation of mitochondrial systems for ATP generation and membrane transport

Simulating intracellular biochemical reactions remains a significant challenge in mathematical modeling because of the complex interactions among diverse molecular species. The natural number simulation (NNS) framework offers a dynamic approach to simulating these reactions using a novel algorithm based on reaction equations. In this study, we developed a computational cell model incorporating mitochondria to examine key metabolic processes, including glucose uptake, glycolysis, the tricarboxylic acid cycle, and ATP synthesis via the electron transport chain. Substrate transport mediated by membrane proteins, such as pyruvate and nicotinamide adenine dinucleotide transporters, and the electron transport chain, was replicated using simplified reaction equations. The simulation results showed that, with appropriately chosen rate constants, the ATP production rate reached approximately 155 molecules s^- 1 per ATP synthase. Sensitivity analysis indicated that the number of mitochondrial phosphate transporters and the rate of phosphate transport into mitochondria strongly influence ATP production. The model also showed that intermittent glucose supply has a minimal impact on ATP production and that the framework is capable of incorporating the effects of deuterium-containing water on ATP synthesis. This framework provides a foundation for future efforts in simulating more detailed metabolic pathways and integrating experimental data.