title: A mathematical model for photoreceptor interactions.
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.
authors.affiliation: Division of Mathematical and Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ 85306, USA. erika.camacho@asu.edu
authors.forename: Erika T
authors.initials: ET
authors.lastname: Camacho
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Colón Vélez
authors.forename: Daniel J
authors.initials: DJ
authors.lastname: Hernández
authors.forename: Ubaldo
authors.initials: U
authors.lastname: Rodríguez Bernier
authors.forename: Jon
authors.initials: J
authors.lastname: Van Laarhoven
authors.forename: Stephen
authors.initials: S
authors.lastname: Wirkus
mesh_terms: D006801:Humans; D008954:Models, Biological; D017949:Retinal Cone Photoreceptor Cells / Q000166:cytology / Q000378:metabolism*; D017948:Retinal Rod Photoreceptor Cells / Q000166:cytology / Q000378:metabolism*