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

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.

[1]  Jo Handelsman,et al.  EPIGENETIC REGULATION OF CELLULAR MEMORY BY THE POLYCOMB AND TRITHORAX GROUP PROTEINS , 2008 .

[2]  B. Harshbarger An Introduction to Probability Theory and its Applications, Volume I , 1958 .

[3]  Jay Neitz,et al.  Topography of long- and middle-wavelength sensitive cone opsin gene expression in human and Old World monkey retina , 2006, Visual Neuroscience.

[4]  J. Mollon,et al.  THE ARRANGEMENT OF L AND M CONES IN HUMAN AND A PRIMATE RETINA , 2003 .

[5]  K. Chung,et al.  Elementary Probability Theory with Stochastic Processes. , 1975 .

[6]  J. Mollon,et al.  The spatial arrangement of cones in the primate fovea , 1992, Nature.

[7]  J. Neitz,et al.  Cone pigment gene expression in individual photoreceptors and the chromatic topography of the retina. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  F. Gonzalez-fernandez,et al.  Zebrafish interphotoreceptor retinoid-binding protein: differential circadian expression among cone subtypes. , 1996, The Journal of experimental biology.

[9]  R. Foster,et al.  Circadian oscillation of photopigment transcript levels in the mouse retina. , 1999, Brain research. Molecular brain research.

[10]  J. Neitz,et al.  Evaluating the human X-chromosome pigment gene promoter sequences as predictors of L:M cone ratio variation. , 2002, Journal of vision.

[11]  A. Hendrickson,et al.  The role of opsin expression and apoptosis in determination of cone types in human retina. , 2004, Experimental eye research.

[12]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[13]  W A Rushton,et al.  Red--grees sensitivity in normal vision. , 1964, Vision research.

[14]  Jeremy Nathans,et al.  Role of a locus control region in the mutually exclusive expression of human red and green cone pigment genes , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[15]  David Williams,et al.  The arrangement of the three cone classes in the living human eye , 1999, Nature.

[16]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[17]  J. Nathans,et al.  Molecular genetics of inherited variation in human color vision. , 1986, Science.

[18]  C. M. Davenport,et al.  Molecular genetics of human blue cone monochromacy. , 1989, Science.

[19]  P. Lennie,et al.  Packing arrangement of the three cone classes in primate retina , 2001, Vision Research.

[20]  Donald J. Zack,et al.  A locus control region adjacent to the human red and green visual pigment genes , 1992, Neuron.

[21]  J. Mollon,et al.  Variations of colour vision in a New World primate can be explained by polymorphism of retinal photopigments , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[22]  D. Baylor,et al.  Spectral sensitivity of cones of the monkey Macaca fascicularis. , 1987, The Journal of physiology.

[23]  J. Neitz,et al.  Variations in cone populations for red–green color vision examined by analysis of mRNA , 1998, Neuroreport.

[24]  R. Marc,et al.  Chromatic organization of primate cones. , 1977, Science.

[25]  Jay Neitz,et al.  Estimates of L:M cone ratio from ERG flicker photometry and genetics. , 2002, Journal of vision.

[26]  F. I. Hárosi Cynomolgus and rhesus monkey visual pigments. Application of Fourier transform smoothing and statistical techniques to the determination of spectral parameters , 1987, The Journal of general physiology.

[27]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[28]  P. Rakić,et al.  Cytogenesis in the monkey retina , 1991, The Journal of comparative neurology.

[29]  Jay Neitz,et al.  Genetic basis of polymorphism in the color vision of platyrrhine monkeys , 1993, Vision Research.

[30]  Drew Williams,et al.  Photopigment transmittance imaging of the primate photoreceptor mosaic , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[31]  Heidi Hofer,et al.  Organization of the Human Trichromatic Cone Mosaic , 2003, The Journal of Neuroscience.

[32]  D. Moazed,et al.  Heterochromatin and Epigenetic Control of Gene Expression , 2003, Science.