A mathematical model for photoreceptor interactions

Erika Camacho, M. A. Colón Vélez Miguel A., Daniel J. Hernández, Ubaldo Rodríguez Bernier, Jon Van Laarhoven, Stephen Wirkus

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The interactions between rods and cones in the retina have been the focus of innumerable experimental and theoretical biological studies in previous decades yet the understanding of these interactions is still incomplete primarily due to the lack of a unified concept of cone photoreceptor organization and its role in retinal diseases. The low abundance of cones in many of the non-primate mammalian models that have been studied make conclusions about the human retina difficult. A more complete knowledge of the human retina is crucial for counteracting the events that lead to certain degenerative diseases, in particular those associated with photoreceptor cell death (e.g., retinitis pigmentosa). In an attempt to gain important insight into the role and interactions of the rods and the cones we develop and analyze a set of mathematical equations that model a system of photoreceptors and incorporate a direct rod-cone interaction. Our results show that the system can exhibit stable oscillations, which correspond to the rhythmic renewal and shedding of the photoreceptors. In addition, our results show the mathematical necessity of this rod-cone direct interaction for survival of both and gives insight into this mechanism.

Original languageEnglish (US)
Pages (from-to)638-646
Number of pages9
JournalJournal of Theoretical Biology
Volume267
Issue number4
DOIs
StatePublished - Dec 21 2010

Fingerprint

Rod-Cone Interaction
cones (retina)
photoreceptors
Retinal Cone Photoreceptor Cells
rods (retina)
Cones
Cone
Theoretical Models
mathematical models
Mathematical Model
Mathematical models
Retina
retina
Interaction
Retinal Diseases
Photoreceptor Cells
Retinitis Pigmentosa
Cell Death
Innumerable
retinal diseases

Keywords

  • Circadian rhythm
  • Limit cycle
  • Rod-derived cone viability factor

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Camacho, E., Colón Vélez Miguel A., M. A., Hernández, D. J., Rodríguez Bernier, U., Van Laarhoven, J., & Wirkus, S. (2010). A mathematical model for photoreceptor interactions. Journal of Theoretical Biology, 267(4), 638-646. https://doi.org/10.1016/j.jtbi.2010.09.006

A mathematical model for photoreceptor interactions. / Camacho, Erika; Colón Vélez Miguel A., M. A.; Hernández, Daniel J.; Rodríguez Bernier, Ubaldo; Van Laarhoven, Jon; Wirkus, Stephen.

In: Journal of Theoretical Biology, Vol. 267, No. 4, 21.12.2010, p. 638-646.

Research output: Contribution to journalArticle

Camacho, E, Colón Vélez Miguel A., MA, Hernández, DJ, Rodríguez Bernier, U, Van Laarhoven, J & Wirkus, S 2010, 'A mathematical model for photoreceptor interactions', Journal of Theoretical Biology, vol. 267, no. 4, pp. 638-646. https://doi.org/10.1016/j.jtbi.2010.09.006
Camacho E, Colón Vélez Miguel A. MA, Hernández DJ, Rodríguez Bernier U, Van Laarhoven J, Wirkus S. A mathematical model for photoreceptor interactions. Journal of Theoretical Biology. 2010 Dec 21;267(4):638-646. https://doi.org/10.1016/j.jtbi.2010.09.006
Camacho, Erika ; Colón Vélez Miguel A., M. A. ; Hernández, Daniel J. ; Rodríguez Bernier, Ubaldo ; Van Laarhoven, Jon ; Wirkus, Stephen. / A mathematical model for photoreceptor interactions. In: Journal of Theoretical Biology. 2010 ; Vol. 267, No. 4. pp. 638-646.
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