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 journalArticlepeer-review

19 Scopus citations


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
Issue number4
StatePublished - Dec 21 2010


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

ASJC Scopus subject areas

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


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