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

Erika Camacho, Thierry Léveillard, José Alain Sahel, Stephen Wirkus

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalBulletin of Mathematical Biology
DOIs
StateAccepted/In press - Jul 21 2016

Fingerprint

rods (retina)
Vertebrate Photoreceptor Cells
cones (retina)
Coexistence
coexistence
Cones
Cone
Theoretical Models
mathematical models
eyes
Glucose
Mathematical Model
Mathematical models
Nutrients
glucose
Enzyme kinetics
Food
mechanism of action
nutrients
Retinitis Pigmentosa

Keywords

  • Holling type III response
  • Photoreceptor co-existence
  • Photoreceptor degeneration
  • Predator-prey
  • Retinitis pigmentosa

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Immunology
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Neuroscience(all)
  • Pharmacology

Cite this

Mathematical Model of the Role of RdCVF in the Coexistence of Rods and Cones in a Healthy Eye. / Camacho, Erika; Léveillard, Thierry; Sahel, José Alain; Wirkus, Stephen.

In: Bulletin of Mathematical Biology, 21.07.2016, p. 1-16.

Research output: Contribution to journalArticle

@article{0bd81873dc1e46cbb7890dcf3982599a,
title = "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",
author = "Erika Camacho and Thierry L{\'e}veillard and Sahel, {Jos{\'e} Alain} and Stephen Wirkus",
year = "2016",
month = "7",
day = "21",
doi = "10.1007/s11538-016-0185-x",
language = "English (US)",
pages = "1--16",
journal = "Bulletin of Mathematical Biology",
issn = "0092-8240",
publisher = "Springer New York",

}

TY - JOUR

T1 - Mathematical Model of the Role of RdCVF in the Coexistence of Rods and Cones in a Healthy Eye

AU - Camacho, Erika

AU - Léveillard, Thierry

AU - Sahel, José Alain

AU - Wirkus, Stephen

PY - 2016/7/21

Y1 - 2016/7/21

N2 - 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.

AB - 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.

KW - Holling type III response

KW - Photoreceptor co-existence

KW - Photoreceptor degeneration

KW - Predator-prey

KW - Retinitis pigmentosa

UR - http://www.scopus.com/inward/record.url?scp=84979261616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979261616&partnerID=8YFLogxK

U2 - 10.1007/s11538-016-0185-x

DO - 10.1007/s11538-016-0185-x

M3 - Article

SP - 1

EP - 16

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

ER -