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An urn model of the development of L/M cone ratios in human and macaque retinas
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.
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“Although there is no experimental data demonstrating a role for epigenetic silencing, the observation that the ratio of L:M pigment messenger RNA changes over the course of development (Knoblauch, Neitz & Neitz, 2006) has led us to suggest a model in which, during gestation, each cone cycles randomly between transcribing either the L or M opsin gene that can explain features of the topography of L”
From The genetics of normal and defective color vision (2011) · cites this paper as Knoblauch et al., 2006
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Cited by
The genetics of normal and defective color vision
Neitz, J., & Neitz, M. (2011) · Vision Research · doi:10.1016/j.visres.2010.12.002 · Cited by 377
Self-citationNucleotide polymorphisms upstream of the X-chromosome opsin gene array tune L:M cone ratio
GUNTHER, K. L., NEITZ, J., & NEITZ, M. (2008) · Visual Neuroscience · doi:10.1017/s0952523808080280 · Cited by 12
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Metadata
- Authors
- KNOBLAUCH, K., NEITZ, M., & NEITZ, J.
- Venue
- Visual Neuroscience
- Publisher
- Maximum Academic Press
- Published
- 2006-05
- Volume
- 23
- Issue
- 3-4
- Pages
- 387-394
- ISSN
- 0952-5238
- 1469-8714
- Cited by
- 16
- References
- 0
- Language
- en
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