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William Bell | Applied Mathematics, University of Waterloo
Mathematical Models of Mitochondria in the Kidney and Liver
Mitochondria are a key player in several kinds of tissue injury, and are even the ultimate cause of certain diseases. In this work we introduce new models of mitochondrial ATP generation in multiple tissues, including liver hepatocytes and the medullary thick ascending limb in the kidney. Using this model, we predict these tissues' responses to hypoxia, uncoupling, ischemia-reperfusion, and oxidative phosphorylation dysfunction. Our results suggest mechanisms explaining differences in robustness of mitochondrial function across tissues.
The medullary thick ascending limb and proximal tubule in the kidney both experience a high metabolic demand, while having lower baseline activity of oxidative phosphorylation relative to the liver. These factors make these tissues susceptible to dysfunction of Complex III. A lower baseline oxygen tension observed in the thick ascending limb makes it susceptible to Complex IV. On the other hand, since the liver lacks these risk factors, and has higher baseline rates of glycolysis, it is less susceptible to all kinds of oxidative phosphorylation dysfunction.
Ischemia-reperfusion is an intriguing example of a non-equilibrium behaviour driven by a change in tissue oxygen tension. Ischemia involves prolonged hypoxia, followed by the sudden return of oxygen during reperfusion. During reperfusion, we predict that the build up of succinate causes the electron transport chain in the liver to temporarily be in a highly reduced state. This can lead to the production of reactive oxygen species. We accurately predict the timescale on which the electron transport chain is left in a reduced state, and we observe levels of reduction likely to lead to reactive oxygen species production.
Aside from the above, we predict thresholds for ATP depletion from hypoxia, and we predict the consequences for oxygen consumption of uncoupling. We find that once again, the kidney tissues considered are more at risk from hypoxia. We predict that hypoxia represents a danger of ATP depletion in the proximal tubule below 10 mmHg of oxygen partial pressure, and in the thick ascending limb below 3 mmHg.
We examine at length the effects of diabetes on the liver and kidney, and we find that it may leave the kidney especially at greater risk for ATP depletion and reactive oxygen species formation. This is particularly true during hypoxia (and uncoupling in the case of ATP depletion).
Our modelling efforts indicate the viability of modelling mitochondrial pathologies with mechanistic models. We demonstrate that even simple models of mitochondrial dysfunction may effectively reproduce experimental results.