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An Age-dependent Feedback Control Model for Calcium and Reactive Oxygen Species in Yeast Cells

Calcium and reactive oxygen species (ROS) interact with each other and play an important role in cell signaling networks. Based on the existing mathematical models, we develop an age-dependent feedback control model to simulate the interaction. The model consists of three subsystems: cytosolic calcium dynamics, ROS generation from the respiratory chain in mitochondria, and mitochondrial energy metabolism. In the model, we hypothesized that ROS induces calcium release from the yeast endoplasmic reticulum , Golgi apparatus, and vacuoles, and that ROS damages calmodulin and calcineurin by oxidizing them. The dependence of calcium uptake by Vcx1p on ATP is incorporated into the model. The model can approximately reproduce the log phase calcium dynamics. The simulated interaction between the cytosolic calcium and mitochondrial ROS shows that an increase in calcium results in a decrease in ROS initially (in log phase), but the increase-decrease relation is changed to an increase-increase relation when the cell is getting old. This could accord with the experimental observation that calcium diminishes ROS from complexes I and III of the respiratory chain under normal conditions, but enhances ROS when the complex formations are inhibited. The model predicts that the subsystem of the calcium regulators Pmc1p, Pmr1p, and Vex1p is stable, controllable, and observable. These structural properties of the dynamical system could mathematically confirm that cells have evolved delicate feedback control mechanisms to maintain their calcium homeostasis.

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