1. An urn model of the development of L/M cone ratios in human and macaque retinas
- Author
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Kenneth Knoblauch, Jay Neitz, Maureen Neitz, Cerveau et vision, Institut National de la Recherche Agronomique (INRA)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-IFR19-Institut National de la Santé et de la Recherche Médicale (INSERM), Department of Cell Biology, Neurobiology and Anatomy, Department of Ophthalmology, Medical College of Wisconsin, and Knoblauch, Kenneth
- Subjects
Male ,Opsin ,genetic structures ,Physiology ,Color vision ,MESH: Cones (Retina) ,[SDV.GEN] Life Sciences [q-bio]/Genetics ,Type (model theory) ,Biology ,Models, Biological ,Macaque ,Retina ,Article ,Combinatorics ,Models ,MESH: Markov Chains ,biology.animal ,[SDV.BDD] Life Sciences [q-bio]/Development Biology ,Animals ,Humans ,MESH: Animals ,Cones (Retina) ,[SDV.MHEP.OS]Life Sciences [q-bio]/Human health and pathology/Sensory Organs ,[SDV.BDD]Life Sciences [q-bio]/Development Biology ,[SDV.GEN]Life Sciences [q-bio]/Genetics ,MESH: Humans ,MESH: Retina ,MESH: Macaca ,Rod Opsins ,MESH: Models, Biological ,State (functional analysis) ,Cone (category theory) ,Anatomy ,Biological ,Markov Chains ,Sensory Systems ,MESH: Male ,[SDV.MHEP.OS] Life Sciences [q-bio]/Human health and pathology/Sensory Organs ,Retinal Cone Photoreceptor Cells ,Ball (bearing) ,Macaca ,Female ,Development (differential geometry) ,MESH: Opsin ,sense organs ,MESH: Female - Abstract
A model of the development ofL/Mcone ratios in the Old World primate retina is presented. It is supposed that during gestation, the cone cycles randomly between states in which it transcribes eitherLorMopsin. The current state determines and increases the probability that it will transcribe the same opsin in future cycles. These assumptions are sufficient to formalize the process as a Markov chain that can be modeled as an urn containing two types of balls,LandM. Drawing one ball results in the increase of its species and the decrease of the other. Over the long run, the urn will become populated with a single type of ball. This state corresponds to the photoreceptor adopting a fixed identity for its lifetime. We investigate the effect of the number of states and the rule that regulates the advantage of transition toward one cone type or another on the relation between fetal and adultL/Mcone ratios. In the range of 100 to 1000 states, small variations of the initialL/Mratio or the transition advantage can each generate large changes in the finalL/Mratio, in qualitative accord with the variation seen in human adult retinas. The time course to attain stableL/Mratios also varies with these parameters. If it is believed that the cycling follows a circadian rhythm, then finalL/Mcone ratios would be expected to stabilize shortly after birth in the human being and the macaque.
- Published
- 2006
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