MATHEMATICAL MODELING OF RETINAL DEGENERATION: AEROBIC GLYCOLYSIS IN A SINGLE CONE

Abstract

Cell degeneration, including that resulting in retinal diseases, is linked to metabolic issues. In the retina, photoreceptor degeneration can result from imbalance in lactate production and consumption as well as disturbances to pyruvate and glucose levels. To identify the key mechanisms in metabolism that may be culprits of this degeneration, we use a nonlinear system of differential equations to mathematically model the metabolic pathway of aerobic glycolysis in a healthy cone photoreceptor. This model allows us to analyze the levels of lactate, glucose, and pyruvate within a single cone cell. We perform numerical simulations, use available metabolic data to estimate parameters and fit the model to this data, and conduct a sensitivity analysis using two different methods (LHS/PRCC and eFAST) to identify pathways that have the largest impact on the system. Using bifurcation techniques, we find that the system has a bistable regime, biologically corresponding to a healthy versus a pathological state. The system exhibits a saddle node bifurcation and hysteresis. This work confirms the necessity for the external glucose concentration to sustain the cell even at low initial internal glucose levels. It also validates the role of {beta}-oxidation of fatty acids which fuel oxidative phosphorylation under glucose- and lactate-depleted conditions, by showing that the rate of {beta}-oxidation of ingested outer segment fatty acids in a healthy cone cell must be low. Model simulations reveal the modulating effect of external lactate in bringing the system to steady state; the bigger the difference between external lactate and initial internal lactate concentrations, the longer the system takes to achieve steady state. Parameter estimation for metabolic data demonstrates the importance of rerouting glucose and other intermediate metabolites to produce glycerol 3-phosphate (G3P), thus increasing lipid synthesis (a precursor to fatty acid production) to support their high growth rate. While a number of parameters are found to be significant by one or both of the methods for sensitivity analysis, the rate of {beta}-oxidation of ingested outer segment fatty acids is shown to consistently play an important role in the concentration of glucose, G3P, and pyruvate, whereas the extracellular lactate level is shown to consistently play an important role in the concentration of lactate and acetyl coenzyme A. The ability of these mechanisms to affect key metabolites variability and levels (as revealed in our analyses) signifies the importance of inter-dependent and inter-connected feedback processes modulated by and affecting both the RPEs and cones metabolism.