Mitochondrial dysfunction can result from several factors, including oxidative stress. Mitochondria are major producers of reactive oxygen species (ROS) through a process that is sensitive to the proton motive force and regulated by scavenging enzymes (SE) and the activation of uncoupling proteins (UCP), which decrease DeltaPsi. The tissue-damaging effects of ROS are hypothesized to underlie many well-defined diseases and clinically-relevant complications, including those associated with diabetes, Parkinson's, Alzheimer's, myopathy, and atherosclerosis. ROS have also been shown to play important signaling roles in mitochondrial biogenesis, longevity, and mitochondrial evolution and adaptation. Therefore, tight regulation of ROS is important to minimize damage without impacting important signaling functions. Pancreatic beta-cells are energy-sensing cells because they sense the ambient plasma-glucose concentration and secrete insulin to signal other tissues to take up glucose. An increase in plasma-glucose levels leads to an increase in the fluxes through the glycolytic and mitochondrial metabolism pathways and an increase in the cellular ATP-to-ADP ratio. This causes a series of events to occur, in which ATP-sensitive potassium channels close, voltage-gated calcium channels open, and insulin secretion is triggered. Environmental factors, such as low physical activity and hypercaloric lipid-rich diets, can lead to decreased glucose-induced insulin secretion in the long term citeNL01, and there is evidence to suggest that ROS and the activity of uncoupling proteins play a key role in determining $beta$-cell dysfunction under these conditions. A long-term positive energy balance, where energy intake exceeds energy expenditure, is the leading cause of insulin resistance, as homeostatic mechanisms are gradually overwhelmed citeKP06a. Challenging mitochondria with chronically large physiological amounts of nutrients, i.e., glucose and fatty acids, leads to an accumulation of ROS damage, negatively affecting mitochondrial function. Such age acquired reductions as well as genetically inherited reductions in mitochondrial function and density have been shown to predispose individuals to insulin resistance and type 2 diabetes. Thus, insights into the effects of ROS on mitochondrial function will be central to our understanding of issues pertaining to diets, exercise regimens, and the current obesity epidemic. To investigate mitochondrial ROS production in response to nutrient inputs, we developed a simplified mathematical model based on models derived from first principles and the current published data. The model captures the behavior of mitochondrial respiration and ATP synthesis in pancreatic beta-cells, and goes beyond the previously developed models to include dynamics related to ROS production and the scavenging enzyme and uncoupling protein defense mechanisms. We validate the model by comparing predictions to experimental results of proton leak from the literature, and use the model to investigate the effects of uncoupling proteins and mitochondrial density on ROS and ATP production responses to glucose (results section). The model we developed goes beyond the models upon which it was based by incorporating ROS production and the activity of scavenging enzymes and uncoupling proteins. Its simplicity is an advantage in that it allows easy manipulation and transference (i.e., through parameter adjustments), making it useful in pursuing research investigating the integrative physiology of mitochondria. The model is capable of capturing the non-ohmic behavior of the proton-leak rate as a function of membrane potential. Also, having been developed for pancreatic beta-cell mitochondria, the model allows us to make inferences and propose hypotheses related to insulin secretion and the effects of diet and exercise. These results are relevant to complications presented in patients with diabetes and impaired glucose-stimulated insulin secretion. Emerging evidence supports the hypothesis that mitochondrial dysfunction causes insulin resistance and hyperglycemia: prominent features of type 2 diabetes citeBL05. Such analyses have emphasized the critical roles of mitochondrial fatty acid oxidation, mitochondrial density, and uncoupling protein activity in disease progression. The results shown here suggest a pathway by which increases in ROS overproduction in relation to ATP production can potentially contribute to mitochondrial dysfunction through age-associated accumulation of damage from ROS and decreases in mitochondrial density through autophagy. Rates of fatty acid oxidation will be incorporated in the model in future work to investigate the role of fatty acids in ROS production and insulin secretion.
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