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K. Knoblauch, M. Neitz, J. Neitz; An Urn Model of the Development of Macaque and Human Adult L:M Cone Ratios . Invest. Ophthalmol. Vis. Sci. 2005;46(13):4632.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: In Old World primates, including humans, fetal and adult retinas differ dramatically in L:M pigment mRNA ratio. There is also tremendous variation in the adult L:M cone ratio. A simple model that explains these observations involves a dynamic competition between the L and M gene promoters for interaction with the locus control region (LCR) in which each time the LCR/promoter complex is disrupted, the promoters compete anew. When a promoter is not interacting with the LCR, it is exposed to gene silencing. Thus, in an incipient L/M cone, each LCR/promoter interaction changes the relative probabilities that L vs M will win in the next round of competition until, finally, the probability of association with one or the other promoter is reduced to zero. Methods: The process was modeled as an urn containing an initial ratio of L:M balls. When an L–ball is drawn, r L–balls are added and r M–balls withdrawn; when an M is drawn s M–balls are added and s L balls withdrawn. These parameters with the total number of balls, N, specify a Markov chain with transition matrix of N+1 states, including two absorbing states (for each of L and M). The transition matrix determines the final L:M distribution in which each ball is either L or M. Results: The curve relating final to initial %L–cones is sigmoidal. Changing the L/M replacement rule for a fixed number of states produces parallel shifts along the axis of initial %L. Increasing the number of states (balls in the urn) steepens the curve. A 100–ball urn requires a replacement rule of 8/1 for macaque and 2.5/1 for humans to predict the correct final ratios from the initial ratios. For human, the final %L varies from about 0.35 to 0.95 as the replacement rule varies from 2/1 to 4/1. Ninety–nine percent of the cones are committed as L or M in 68 steps for macaque and 84 for human. Thus, the process would near completion at birth for each species if the LCR dissociates once per day. Conclusions: The model predicts that subtle individual differences at the photopigment gene locus that would produce small changes in the dynamics of the competition occurring during development could explain large individual differences in adult cone ratio.
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