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An urn model of the development of L/M cone ratios in human and macaque retinas

Published online by Cambridge University Press:  06 September 2006

KENNETH KNOBLAUCH ,
MAUREEN NEITZ  and
JAY NEITZ
KENNETH KNOBLAUCH
Affiliation:
Inserm, U371, Cerveau et Vision, Department of Cognitive Neuroscience, Bron F-69500, France Université Claude Bernard Lyon 1, Institut F éderatif des Neurosciences (IFR 19), Bron, France
MAUREEN NEITZ
Affiliation:
Department of Cell Biology, Neurobiology, and Anatomy and Department of Ophthalmology, Medical College of Wisconsin, Milwaukee, Wisconsin
JAY NEITZ
Affiliation:
Department of Cell Biology, Neurobiology, and Anatomy and Department of Ophthalmology, Medical College of Wisconsin, Milwaukee, Wisconsin
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Abstract

A model of the development of L/M cone 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 either L or M opsin. 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, L and M. 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 adult L/M cone ratios. In the range of 100 to 1000 states, small variations of the initial L/M ratio or the transition advantage can each generate large changes in the final L/M ratio, in qualitative accord with the variation seen in human adult retinas. The time course to attain stable L/M ratios also varies with these parameters. If it is believed that the cycling follows a circadian rhythm, then final L/M cone ratios would be expected to stabilize shortly after birth in the human being and the macaque.

Keywords

L/M cone ratioprimate retinal developmentcolor visionMarkov chainUrn model
Type
GENETICS
Information
Visual Neuroscience , Volume 23 , Issue 3-4 , May 2006 , pp. 387 - 394
Copyright
© 2006 Cambridge University Press

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