Mathematical Model of the Role of RdCVF in the Coexistence of Rods and Cones in a Healthy Eye

Abstract

Understanding the essential components and processes for coexistence of rods and cones is at the forefront of retinal research. The recent discovery on RdCVF's mechanism and mode of action for enhancing cone survival brings us a step closer to unraveling key questions of coexistence and codependence of these neurons. In this work, we build from ecological and enzyme kinetic work on functional response kinetics and present a mathematical model that allows us to investigate the role of RdCVF and its contribution to glucose intake. Our model results and analysis predict a dual role of RdCVF for enhancing and repressing the healthy coexistence of the rods and cones. Our results show that maintaining RdCVF above a threshold value allows for coexistence. However, a significant increase above this value threatens the existence of rods as the cones become extremely efficient at uptaking glucose and begin to take most of it for themselves. We investigate the role of natural glucose intake and that due to RdCVF in both high and low nutrient levels. Our analysis reveals that under low nutrient levels coexistence is not possible regardless of the amount of RdCVF present. With high nutrient levels coexistence can be achieved with a relative small increase in glucose uptake. By understanding the contributions of rods to cones survival via RdCVF in a non-diseased retina, we hope to shed light on degenerative diseases such as retinitis pigmentosa.

Keywords: Holling type III response; Photoreceptor co-existence; Photoreceptor degeneration; Predator-prey; Retinitis pigmentosa.