Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T02:07:04.991Z Has data issue: false hasContentIssue false
  • English
  • Français

Homotypic constraints dominate positioning of on- and off-center beta retinal ganglion cells

Published online by Cambridge University Press:  03 February 2006

STEPHEN J. EGLEN ,
PETER J. DIGGLE  and
JOHN B. TROY
STEPHEN J. EGLEN
Affiliation:
Department for Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge UK
PETER J. DIGGLE
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
JOHN B. TROY
Affiliation:
Biomedical Engineering Department, Northwestern University, Evanston, Illinois
Get access Rights & Permissions [Opens in a new window]

Abstract

Beta retinal ganglion cells (RGCs) of the cat are classified as either on-center or off-center, according to their response to light. The cell bodies of these on- and off-center RGCs are spatially distributed into regular patterns, known as retinal mosaics. In this paper, we investigate the nature of spatial dependencies between the positioning of on- and off-center RGCs by analysing maps of RGCs and simulating these patterns. We introduce principled approaches to parameter estimation, along with likelihood-based techniques to evaluate different hypotheses. Spatial constraints between cells within-type and between-type are assumed to be controlled by two univariate interaction functions and one bivariate interaction function. By making different assumptions on the shape of the bivariate interaction function, we can compare the hypothesis of statistical independence against the alternative hypothesis of functional independence, where interactions between type are limited to preventing somal overlap. Our findings suggest that the mosaics of on- and off-center beta RGCs are likely to be generated assuming functional independence between the two types. By contrast, allowing a more general form of bivariate interaction function did not improve the likelihood of generating the observed maps. On- and off-center beta RGCs are therefore likely to be positioned subject only to homotypic constraints and the physical constraint that no two somas of opposite type can occupy the same position.

Keywords

Beta retinal ganglion cellsRetinal mosaicsFunctional independenceStatistical independencePIPP model
Type
Research Article
Information
Visual Neuroscience , Volume 22 , Issue 6 , November 2005 , pp. 859 - 871
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahnelt, P.K., Fernändez, E., Martinez, O., Bolea, J.A., & Kübber-Heiss, A. (2000). Irregular S-cone mosaics in felid retinas. Spatial interaction with axonless horizontal cells, revealed by cross correlation. Journal of the Optical Society of America A 17, 580–588.Google Scholar
Baddeley, A. & Turner, R. (2000). Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.CrossRefGoogle Scholar
Baddeley, A. & Turner, R. (2005). Spatstat: An R package for analyzing spatial point patterns. Journal of Statistical Software 12, 1–42.Google Scholar
Barnard, G.A. (1963). Contribution to the discussion of Professor Bartlett's paper. Journal of the Royal Statistical Society B 25, 294.Google Scholar
Besag, J.E. (1978). Some methods of statistical analysis for spatial data. Bulletin of the International Statistical Institute 47 (Book 2), 77–92.Google Scholar
Bodnarenko, S.R. & Chalupa, L.M. (1993). Stratification of ON and OFF ganglion cell dendrites depends on glutamate-mediated afferent activity in the developing retina. Nature 364, 144–146.CrossRefGoogle Scholar
Boycott, B.B. & Wässle, H. (1974). The morphological types of ganglion cells of the domestic cat's retina. Journal of Physiology 240, 397–419.CrossRefGoogle Scholar
Cellerino, A., Novelli, E., & Galli-Resta, L. (2000). Retinal ganglion cells with NADPH-diaphorase activity in the chick form a regular mosaic with a strong dorsoventral asymmetry that can be modelled by a minimal spacing rule. European Journal of Neuroscience 12, 613–620.CrossRefGoogle Scholar
Chichilnisky, E.J. & Kalmar, R.S. (2002). Functional asymmetries in on and off ganglion cells of primate retina. Journal of Neuroscience 22, 2737–2747.Google Scholar
Cook, J.E. (1996). Spatial properties of retinal mosaics: An empirical evaluation of some existing measures. Visual Neuroscience 13, 15–30.CrossRefGoogle Scholar
Cook, J.E. & Chalupa, L.M. (2000). Retinal mosaics: New insights into an old concept. Trends in Neuroscience 23, 26–34.CrossRefGoogle Scholar
Cook, J.E. & Podugolnikova, T.A. (2001). Evidence for spatial regularity among retinal ganglion cells that project to the accessory optic system in a frog, a reptile, a bird, and a mammal. Visual Neuroscience 18, 289–297.CrossRefGoogle Scholar
Diggle, P.J. (1986). Displaced amacrine cells in the retina of a rabbit: Analysis of a bivariate spatial point pattern. Journal of Neuroscience Methods 18, 115–125.CrossRefGoogle Scholar
Diggle, P.J. (2002). Statistical Analysis of Spatial Point Patterns, second edition. London: Edward Arnold.
Diggle, P.J., Eglen, S.J., & Troy, J.B. (2005). Modelling the bivariate spatial distribution of amacrine cells. In Case Studies in Spatial Point Process Modelling, ed. Baddeley, A., Gregori, P., Mateu, J., Stoica, R. & Stoyan, D. Lecture Notes in Statistics 185. Springer (in press).
Eglen, S.J. & Willshaw, D.J. (2002). Influence of cell fate mechanisms upon retinal mosaic formation: A modelling study. Development 129, 5399–5408.CrossRefGoogle Scholar
Eglen, S.J., van Ooyen, A., & Willshaw, D.J. (2000). Lateral cell movement driven by dendritic interactions is sufficient to form retinal mosaics. Network: Computation in Neural Systems 11, 103–118.CrossRefGoogle Scholar
Eglen, S.J., Raven, M.A., Tamrazian, E., & Reese, B.E. (2003). Dopaminergic amacrine cells in the inner nuclear layer and ganglion cell layer comprise a single functional retinal mosaic. Journal of Comparative Neurology 466, 343–355.CrossRefGoogle Scholar
Enroth-Cugell, C. & Robson, J.G. (1966). The contrast sensitivity of retinal ganglion cells of the cat. Journal of Physiology 187, 517–522.CrossRefGoogle Scholar
Famiglietti, Jr., E.V. & Kolb, H. (1976). Structural basis for ON- and OFF-center responses in retinal ganglion cells. Science 194, 193–195.CrossRefGoogle Scholar
Galli-Resta, L., Novelli, E., Kryger, Z., Jacobs, G.H., & Reese, B.E. (1999). Modelling the mosaic organization of rod and cone photoreceptors with a minimal-spacing rule. European Journal of Neuroscience 11, 1461–1469.CrossRefGoogle Scholar
Galli-Resta, L., Resta, G., Tan, S.-S., & Reese, B.E. (1997). Mosaics of Islet-1-expressing amacrine cells assembled by short-range cellular interactions. Journal of Neuroscience 17, 7831–7838.Google Scholar
Heikkinen, J. & Penttinen, A. (1999). Bayesian smoothing in the estimation of the pair potential function of Gibbs point processes. Bernoulli 5, 1119–1136.CrossRefGoogle Scholar
Kageyama, G.H. & Wong-Riley, M.T. (1984). The histochemical localization of cytochrome oxidase in the retina and lateral geniculate nucleus of the ferret, cat, and monkey, with particular reference to retinal mosaics and on/off-center visual channels. Journal of Neuroscience 4, 2445–2459.Google Scholar
Kolb, H. & Nelson, R. (1984). Neural architecture of the cat retina. Progress in Retinal Research 3, 21–60.CrossRefGoogle Scholar
Kouyama, N. & Marshak, D.W. (1997). The topographical relationship between two neuronal mosaics in the short wavelength-sensitive system of the primate retina. Visual Neuroscience 14, 159–167.CrossRefGoogle Scholar
Kuffler, S.W. (1953). Discharge patterns and functional organisation of mammalian retina. Journal of Neurophysiology 16, 37–68.Google Scholar
Lohmann, C. & Wong, R.O.L. (2001). Cell-type specific dendritic contacts between retinal ganglion cells during development. Journal of Neurobiology 48, 150–162.CrossRefGoogle Scholar
Lotwick, H.W. & Silverman, B.W. (1982). Methods for analysing spatial processes of several types of points. Journal of the Royal Statistical Society B 44, 406–413.Google Scholar
Nelson, R., Famiglietti, Jr., E.V., & Kolb, H. (1978). Intracellular staining reveals different levels of stratification for on- and off-center ganglion cells in cat retina. Journal of Neurophysiology 41, 472–483.Google Scholar
Peichl, L. (1989). Alpha and delta ganglion cells in the rat retina. Journal of Comparative Neurology 286, 120–139.CrossRefGoogle Scholar
R Development Core Team (2005). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
Raven, M.A., Eglen, S.J., Ohab, J.J., & Reese, B.E. (2003). Determinants of the exclusion zone in dopaminergic amacrine cell mosaics. Journal of Comparative Neurology 461, 123–136.CrossRefGoogle Scholar
Reese, B.E. & Galli-Resta, L. (2002). The role of tangential dispersion in retinal mosaic formation. Progress in Retinal and Eye Research 21, 153–168.CrossRefGoogle Scholar
Ringach, D.L. (2004). Haphazard wiring of simple receptive fields and orientation columns in visual cortex. Journal of Neurophysiology 92, 468–476.CrossRefGoogle Scholar
Ripley, B.D. (1976). The second-order analysis of stationary point processes. Journal of Applied Probability 13, 255–266.CrossRefGoogle Scholar
Ripley, B.D. (1977). Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society B 39, 172–212.Google Scholar
Ripley, B.D. (1979). AS137 Simulating spatial patterns. Applied Statistics 28, 109–112.CrossRefGoogle Scholar
Rockhill, R.L., Euler, T., & Masland, R.H. (2000). Spatial order within but not between types of retinal neurons. Proceedings of the National Academy of Sciences of the U.S.A. 97, 2303–2307.CrossRefGoogle Scholar
Rodieck, R.W. (1991). The density recovery profile: A method for the analysis of points in the plane applicable to retinal studies. Visual Neuroscience 6, 95–111.CrossRefGoogle Scholar
Rodieck, R.W. & Marshak, D.W. (1992). Spatial density and distribution of choline acetyltransferase immunoreactive cells in human, macaque and baboon retinas. Journal of Comparative Neurology 321, 46–64.CrossRefGoogle Scholar
Rowlingson, B.S. & Diggle, P.J. (1993). Splancs: Spatial point pattern analysis code in S-Plus. Computers and Geosciences 19, 627–655.CrossRefGoogle Scholar
Self, S.G. & Liang, K.-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association 82, 605–610.CrossRefGoogle Scholar
Stein, J.J., Johnson, S.A., & Berson, D.M. (1996). Distribution and coverage of beta-cells in the cat retina. Journal of Comparative Neurology 372, 597–617.3.0.CO;2-#>CrossRefGoogle Scholar
Tanemura, M. (1979). On random complete packing by discs. Annals of the Institute of Statistical Mathematics 31, 351–365.CrossRefGoogle Scholar
Wässle, H. & Riemann, H.J. (1978). The mosaic of nerve cells in the mammalian retina. Proceedings of the Royal Society B (London) 200, 441–461.CrossRefGoogle Scholar
Wässle, H., Boycott, B.B., & Illing, R.B. (1981a). Morphology and mosaic of on-beta and off-beta cells in the cat retina and some functional considerations. Proceedings of the Royal Society B (London) 212, 177–195.Google Scholar
Wässle, H., Peichl, L., & Boycott, B.B. (1981b). Morphology and topography of on-alpha and off-alpha cells in the cat retina. Proceedings of the Royal Society B (London) 212, 157–175.Google Scholar
Zhan, X.J. (1996). Properties of ON- and OFF-center beta cell somatic and dendritic mosaics in cat retina. Ph.D. Thesis, Northwestern University, Evanston, Illinois.
Zhan, X.J. & Troy, J.B. (2000). Modeling cat retinal beta-cell arrays. Visual Neuroscience 17, 23–39.CrossRefGoogle Scholar