Insights into pathological mechanisms and interventions revealed by analyzing a mathematical model for cone metabolism

Abstract

This work analyzes a mathematical model for the metabolic dynamics of a cone photoreceptor, which is the first model to account for energy generation from fatty acids oxidation of shed photoreceptor outer segments (POS). Multiple parameter bifurcation analysis shows that joint variations in external glucose, the efficiency of glucose transporter 1 (GLUT1), lipid utilization for POS renewal, and oxidation of fatty acids affect the cone's metabolic vitality and its capability to adapt under glucose-deficient conditions. The analysis further reveals that when glucose is scarce cone viability cannot be sustained by only fueling energy production in the mitochondria, but it also requires supporting anabolic processes to create lipids necessary for cell maintenance and repair. In silico experiments are used to investigate how the duration of glucose deprivation impacts the cell without and with a potential GLUT1 or oxidation of fatty acids intervention as well as a dual intervention. The results show that for prolonged duration of glucose deprivation, the cone metabolic system does not recover with higher oxidation of fatty acids and requires greater effectiveness of GLUT1 to recover. Finally, time-varying global sensitivity analysis is applied to assess the sensitivity of the model outputs of interest to changes and uncertainty in the parameters at specific times. The results reveal a critical temporal window where there would be more flexibility for interventions to rescue a cone cell from the detrimental consequences of glucose shortage.

Mathematical model for glutathione dynamics in the retina

“…GSA is a very useful tool to investigate the qualitative behavior of a mathematical model, and we have applied it previously to a model for cone photoreceptor metabolism 62 , 63 . In this study, GSA is used to examine which of the processes captured in the model for the GSH system are the most important in a control mouse retina compared to degenerative retina with RP.…”

“…GSA is a very useful tool to investigate the qualitative behavior of a mathematical model, and we have applied it previously to a model for cone photoreceptor metabolism 62,63 . In this…”

Advancing treatment of retinal disease through in silico trials

“…Further, these models predicted conditions under which rods and cones can stably coexist, revealing that the assistance provided to the cones by the rods via a trophic factor is crucial in this respect [47,49,70,298]. This group's retinal metabolic models are the most biochemically detailed to have been generated to date, using sensitivity and bifurcation analyses to determine which processes are most important in maintaining a healthy homeostasis [16,52,54,81]. Under RP conditions, their models clarify and elucidate the stages of retinal degeneration that may be traced on the road to complete atrophy, highlighting which processes must change to allow progression to the next stage [46,50,51].…”

“…For example, Roberts et al [247,248]'s models of hyperoxia-driven photoreceptor degeneration in RP could be applied to any retinal disease in which oxygen toxicity is thought to play a role in driving cell death (e.g. AMD), while Aparicio et al [16], Camacho et al [52,54], Dobreva et al [81]'s metabolic models capture processes which are fundamental both in maintaining a healthy retinal homeostasis and in driving a range of retinal diseases, including RP and AMD. The increasing availability of clinical imaging data, especially SD-OCT and OCTA, together with a rise in omics data will furnish future modelling studies with a wealth of physiological and biochemical information, guiding model development, facilitating more detailed model testing and validation, and paving the way for ISCTs.…”