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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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References

REFERENCES

Baylor, D.A., Nunn, B.J., & Schnapf, J.L. (1987). Spectral sensitivity of cones of the monkey Macaca fascicularis. Journal of Physiology 390, 145–160.CrossRefGoogle Scholar
Bowmaker, J.K., Mollon, J.D., & Jacobs, G.H. (1983). Microspectrophotometric results for old and new world primates. In Colour Vision, eds. Mollon, J.D. & Sharpe, L.T., pp. 57–68. London: Academic Press.
Bowmaker, J.K., Parry, J.W.L., & Mollon, J.D. (2003). The arrangement of L and M cones in human and a primate retina. In Normal and defective. Colour Vision, eds. Mollon, J.D., Pokorny, J. & Knoblauch, K., pp. 39–50. New York: Oxford University Press.CrossRef
Carroll, J., Neitz, J., & Neitz, M. (2002). Estimates of L:M cone ratio from ERG flicker photometry and genetics. Journal of Vision 2, 531–542.Google Scholar
Chung, K.L. (1974). Elementary Probability Theory with Stochastic Processes. New York: Springer-Verlag.CrossRef
Cornish, E.E., Xiao, M., Yang, Z., Provis, J.M., & Hendrickson, A.E. (2004). The role of opsin expression and apoptosis in determination of cone types in human retina. Experimental Eye Research 78, 1143–1154.CrossRefGoogle Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edition. New York: John Wiley & Sons, Inc.
Grewal, S.I.S. & Moazed, D. (2003). Heterochromatin and epigenetic control of gene expression. Science 301, 798–802.CrossRefGoogle Scholar
Hagstrom, S.A., Neitz, J., & Neitz, M. (1998). Variations in cone populations for red-green color vision examined by analysis of mRNA. Neuroreport 9, 1963–1967.CrossRefGoogle Scholar
Hagstrom, S.A., Neitz, M., & Neitz, J. (2000). Cone pigment gene expression in individual photoreceptors and the chromatic topography of the retina. Journal of the Optical Society of America A (Optics, Image Science and Vision 17, 527–537.CrossRefGoogle Scholar
Harosi, F.I. (1987). Cynomolgus and rhesus monkey visual pigments. Application of Fourier transform smoothing and statistical techniques to the determination of spectral parameters. Journal of General Physiology 89, 717–743.Google Scholar
Hofer, H., Carroll, J., Neitz, J., Neitz, M., & Williams, D.R. (2005). Organization of the human trichromatic cone mosaic. Journal of Neuroscience 25, 9669–9679.CrossRefGoogle Scholar
Jacobs, G.H., Neitz, J., & Neitz, M. (1993). Genetic basis of polymorphism in the color vision of platyrrhine monkeys. Vision Research 33, 269–274.CrossRefGoogle Scholar
LaVail, M.M., Rapaport, D.H., & Rakic, P. (1991). Cytogenesis in the monkey retina. Journal of Comparative Neurology 309, 86–114.CrossRefGoogle Scholar
Marc, R.E. & Sperling, H.G. (1977). Chromatic organization of primate cones. Science 196, 454–456.CrossRefGoogle Scholar
McMahon, C., Hendrickson, A.E., Dacey, D.M., Neitz, J., & Neitz, M. (2000). L-M cone ratio as a function of eccentricity in primate retina estimated from analysis of messenger RNA (ARVO abstract). Investigative Ophthalmology & Visual Science 41, S494.Google Scholar
McMahon, C., Neitz, J., & Neitz, M. (2003). Comparison of human and monkey pigment gene promoters to evaluate DNA sequences proposed to govern L:M cone ratio. In Normal & Defective Colour Vision, eds. Mollon, J.D., Pokorny, J. & Knoblauch, K., pp. 51–59. Oxford: Oxford University Press.CrossRef
McMahon, C., Neitz, J., & Neitz, M. (2004). Evaluating the human X-chromosome pigment gene promoter sequences as predictors of L-M cone ratio variation. Journal of Vision 4, 203–208.Google Scholar
Mollon, J.D. & Bowmaker, J.K. (1992). The spatial arrangement of cones in the primate fovea. Nature 360, 677–679.CrossRefGoogle Scholar
Mollon, J.D., Bowmaker, J.K., & Jacobs, G.H. (1984). Variations of colour vision in a New World primate can be explained by polymorphism of retinal photopigments. Proceedings of the Royal Society B: Biological Sciences 222, 373–399.CrossRefGoogle Scholar
Nathans, J., Davenport, C.M., Maumenee, I.H., Lewis, R.A., Hejtmancik, J.F., Litt, M., Lovrien, E., Weleber, R., Bachynski, B., & Zwas, F. (1989). Molecular genetics of human blue cone monochromacy. Science 245, 831–838.CrossRefGoogle Scholar
Nathans, J., Piantanida, T.P., Eddy, R.L., Shows, T.B., & Hogness, D.S. (1986). Molecular genetics of inherited variation in human color vision. Science 232, 203–210.CrossRefGoogle Scholar
Neitz, M., Balding, S.D., McMahon, C., Sjoberg, S.A., & Neitz, J. (2006). Topography of long- and middle-wavelength sensitive cone opsin gene expression in human and Old World monkey retina. Visual Neuroscience 23, 379–385.CrossRefGoogle Scholar
Packer, O.S., Williams, D.R., & Bensinger, D.G. (1996). Photopigment transmittance imaging of the primate photoreceptor mosaic. Journal of Neuroscience 16, 2251–2260.Google Scholar
R Development Core Team (2005). R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, URL http://www.R-project.org, ISBN 3-900051-07-0.
Rajendran, R.R., Van Niel, E.E., Stenkamp, D.L., Cunningham, L.L., Raymond, P.A., & Gonzalez-Fernandez, F. (1996). Zebrafish interphotoreceptor retinoid-binding protein: differential circadian expression among cone subtypes. Journal of Experimental Biology 199, 2775–2787.Google Scholar
Ringrose, L. & Paro, R. (2004). Epigenetic regulation of cellular memory by the Polycomb and Trithorax group proteins. Annual Review of Genetics 38, 413–443.CrossRefGoogle Scholar
Roorda, A., Metha, A.B., Lennie, P., & Williams D.R. (2001). Packing arrangement of the three cone classes in primate retina. Vision Research 41, 1291–1306.CrossRefGoogle Scholar
Roorda, A. & Williams, D.R. (1999). The arrangement of the three cone classes in the living human eye. Nature 397, 520–522.CrossRefGoogle Scholar
Rushton, W.A. & Baker, H.D. (1964). Red–green sensitivity in normal vision. Vision Research 4, 75–85.CrossRefGoogle Scholar
Smallwood, P.M., Wang, Y., & Nathans, J. (2002). Role of a locus control region in the mutually exclusive expression of human red and green cone pigment genes. Proceedings of the National Academy of Sciences 99, 1008–1011.CrossRefGoogle Scholar
von Schantz, M., Lucas, R.J., & Foster, R.G. (1999). Circadian oscillation of photopigment transcript levels in the mouse retina. Brain Research. Molecular Brain Research 72, 108–114.CrossRefGoogle Scholar
Wang, Y., Macke, J.P., Merbs, S.L., Zack, D.J., Klaunberg, B., Bennett, J., Gearhart, J., & Nathans, J. (1992). A locus control region adjacent to the human red and green visual pigment genes. Neuron 9, 429–440.CrossRefGoogle Scholar