Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T05:32:55.541Z Has data issue: false hasContentIssue false
  • English
  • Français

Parasol cell mosaics are unlikely to drive the formation of structured orientation maps in primary visual cortex

Published online by Cambridge University Press:  30 October 2012

VICTORIA R.A. HORE ,
JOHN B. TROY  and
STEPHEN J. EGLEN
VICTORIA R.A. HORE
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge Computational Biology Institute, University of Cambridge, Cambridge, UK
JOHN B. TROY
Affiliation:
Department of Biomedical Engineering, Northwestern University, Road Evanston, Illinois
STEPHEN J. EGLEN*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge Computational Biology Institute, University of Cambridge, Cambridge, UK
*
*Address correspondence and reprint requests to: Stephen J. Eglen, Department of Applied Mathematics and Theoretical Physics, Cambridge Computational Biology Institute, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The receptive fields of on- and off-center parasol cell mosaics independently tile the retina to ensure efficient sampling of visual space. A recent theoretical model represented the on- and off-center mosaics by noisy hexagonal lattices of slightly different density. When the two lattices are overlaid, long-range Moiré interference patterns are generated. These Moiré interference patterns have been suggested to drive the formation of highly structured orientation maps in visual cortex. Here, we show that noisy hexagonal lattices do not capture the spatial statistics of parasol cell mosaics. An alternative model based upon local exclusion zones, termed as the pairwise interaction point process (PIPP) model, generates patterns that are statistically indistinguishable from parasol cell mosaics. A key difference between the PIPP model and the hexagonal lattice model is that the PIPP model does not generate Moiré interference patterns, and hence stimulated orientation maps do not show any hexagonal structure. Finally, we estimate the spatial extent of spatial correlations in parasol cell mosaics to be only 200–350 μm, far less than that required to generate Moiré interference. We conclude that parasol cell mosaics are too disordered to drive the formation of highly structured orientation maps in visual cortex.

Keywords

Hexagonal latticesRetinal mosaicsReceptive fieldsOrientation selectivityPIPP model
Type
Review Articles
Information
Visual Neuroscience , Volume 29 , Issue 6 , November 2012 , pp. 283 - 299
Copyright
Copyright © Cambridge University Press 2012

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

Berdondini, L., Imfeld, K., Maccione, A., Tedesco, M., Neukom, S., Koudelka-Hep, M. & Martinoia, S. (2009). Active pixel sensor array for high spatio-temporal resolution electrophysiological recordings from single cell to large scale neuronal networks. Lab on a Chip 9, 2644–2651.CrossRefGoogle ScholarPubMed
Berman, M. & Diggle, P.J. (1989). Estimating weighted integrals of the second-order intensity of spatial point patterns. Journal of the Royal Statistical Society. Series B, Statistical Methodology 51, 81–92.Google 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. The European Journal of Neuroscience 12, 613–620.CrossRefGoogle Scholar
Cook, J.E. (1996). Spatial properties of retinal mosaics: An empirical evaluation of some existing measures. Visual Neuroscience 13, 15–30.CrossRefGoogle ScholarPubMed
Dacey, D.M. (1993). The mosaic of midget ganglion cells in the human retina. The Journal of Neuroscience 13, 5334–5355.CrossRefGoogle ScholarPubMed
Dacey, D.M. & Petersen, M.R. (1992). Dendritic field size and morphology of midget and parasol ganglion cells of the human retina. Proceedings of the National Academy of Sciences of the United States of America 89, 9666–9670.CrossRefGoogle ScholarPubMed
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 ScholarPubMed
Diggle, P.J., Eglen, S.J. & Troy, J.B. (2006). Modelling the bivariate spatial distribution of amacrine cells. In Case Studies in Spatial Point Process Modeling, Vol. 185 of Springer Lecture Notes in Statistics, ed. Baddeley, A., Gregori, P., Mateu, J., Stoica, R. & Stoyan, D., pp. 215–233. New York: Springer.CrossRefGoogle Scholar
Eglen, S.J. (2006). Development of regular cellular spacing in the retina: Theoretical models. Mathematical Medicine and Biology 23, 79–99.CrossRefGoogle ScholarPubMed
Eglen, S.J. (2012). Cellular spacing: Analysis and modelling of retinal mosaics. In Computational Systems Neurobiology, Chapter 12, ed. Le Novére, N., pp. 365–385. New York: Springer.CrossRefGoogle Scholar
Eglen, S.J., Diggle, P.J. & Troy, J.B. (2005). Homotypic constraints dominate positioning of on- and off-centre beta retinal ganglion cells. Visual Neuroscience 22, 859–871.CrossRefGoogle Scholar
Eglen, S.J. & Wong, J.C.T. (2008). Spatial constraints underlying the retinal mosaics of two types of horizontal cells in cat and macaque. Visual Neuroscience 25, 209–214.CrossRefGoogle ScholarPubMed
Field, G.D. & Chichilnisky, E.J. (2007). Information processing in the primate retina: Circuitry and coding. Annual Review of Neuroscience 30, 1–30.CrossRefGoogle ScholarPubMed
Fortune, S.J. (1987). A sweepline algorithm for Voronoi diagrams. Algorithmica 2, 153–172.CrossRefGoogle Scholar
Furrer, R., Nychka, D. & Sain, S. (2011). fields: Tools for Spatial Data. R package version 6.6. http://CRAN.R-project.org/package=fields.Google Scholar
Galli-Resta, L. (2002). Putting neurons in the right places: Local interactions in the genesis of retinal architecture. Trends in Neurosciences 25, 638–643.CrossRefGoogle ScholarPubMed
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. The European Journal of Neuroscience 11, 1461–1469.CrossRefGoogle ScholarPubMed
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. The Journal of Neuroscience 17, 7831–7838.CrossRefGoogle ScholarPubMed
Gauthier, J.L., Field, G.D., Sher, A., Greschner, M., Shlens, J., Litke, A.M. & Chichilnisky, E.J. (2009). Receptive fields in primate retina are coordinated to sample visual space more uniformly. PLoS Biology 7, e1000063.CrossRefGoogle ScholarPubMed
Genz, A. & Azzalini, A. (2011). mnormt: The Multivariate Normal and t Distributions. R package version 1.4-3. http://CRAN.R-project.org/package=mnormt.Google Scholar
Hore, V.R.A. (2011). Do retinal ganglion cell mosaics generate pinwheel structure in the visual cortex?Masters Thesis, University of Cambridge.Google Scholar
Huberman, A.D., Feller, M.B. & Chapman, B. (2008). Mechanisms underlying development of visual maps and receptive fields. Annual Review of Neuroscience 31, 479–509.CrossRefGoogle ScholarPubMed
Kay, J.N., Chu, M.W. & Sanes, J.R. (2012). MEGF10 and MEGF11 mediate homotypic interactions required for mosaic spacing of retinal neurons. Nature 483, 465–469.CrossRefGoogle ScholarPubMed
Kram, Y.A., Mantey, S. & Corbo, J.C. (2010). Avian cone photoreceptors tile the retina as five independent, self-organizing mosaics. PLoS One 5, e8992.CrossRefGoogle ScholarPubMed
Paik, S.-B. & Ringach, D.L. (2011). Retinal origin of orientation maps in visual cortex. Nature Neuroscience 14, 919–925.CrossRefGoogle ScholarPubMed
Paik, S.-B. & Ringach, D.L. (2012). Link between orientation and retinotopic maps in primary visual cortex. Proceedings of the National Academy of Sciences of the United States of America 109, 7091–7096.CrossRefGoogle ScholarPubMed
Perry, V.H., Oehler, R. & Cowey, A. (1984). Retinal ganglion cells that project to the dorsal lateral geniculate nucleus in the macaque monkey. Neuroscience 12, 1101–1123.CrossRefGoogle Scholar
R Development Core Team. (2011). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0.Google 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 ScholarPubMed
Ringach, D.L. (2004). Haphazard wiring of simple receptive fields and orientation columns in visual cortex. Journal of Neurophysiology 92, 468–476.CrossRefGoogle ScholarPubMed
Ringach, D.L. (2007). On the origin of the functional architecture of the cortex. PLoS One 2, e251.CrossRefGoogle ScholarPubMed
Ripley, B.D. (1976). The second-order analysis of stationary point processes. Journal of Applied Probability 13, 255–266.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 United States of America 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 ScholarPubMed
Rowlingson, B.S. & Diggle, P.J. (1993). SPLANCS: Spatial point pattern analysis code in S-Plus. Computers and Geosciences 19, 627–655.CrossRefGoogle Scholar
Schnabel, M., Kaschube, M., Löwel, S. & Wolf, F. (2007). Random waves in the brain: Symmetries and defect generation in the visual cortex. The European Physical Journal 145, 137–157.Google Scholar
Sirotin, Y.B. & Das, A. (2010). Zooming in on mouse vision. Nature Neuroscience 13, 1045–1046.CrossRefGoogle Scholar
Soodak, R.E. (1987). The retinal ganglion cell mosaic defines orientation columns in striate cortex. Proceedings of the National Academy of Sciences of the United States of America 84, 3936–3940.CrossRefGoogle ScholarPubMed
Swindale, N.V. (1996). The development of topography in the visual cortex: A review of models. Network: Computation in Neural Systems 7, 161–247.CrossRefGoogle ScholarPubMed
Tanemura, M. (2003). Statistical distributions of Poisson Voronoi cells in two and three dimensions. Forma 18, 221–247.Google Scholar
Wässle, H., Boycott, B.B. & Illing, R.B. (1981 a). Morphology and mosaic of on-beta and off-beta cells in the cat retina and some functional considerations. Proceedings of the Royal Society of London. Series B, Biological Sciences 212, 177–195.Google ScholarPubMed
Wässle, H., Peichl, L. & Boycott, B.B. (1981 b). Morphology and topography of on-alpha and off-alpha cells in the cat retina. Proceedings of the Royal Society of London. Series B, Biological Sciences 212, 157–175.Google ScholarPubMed
Wässle, H. & Riemann, H.J. (1978). The mosaic of nerve cells in the mammalian retina. Proceedings of the Royal Society of London. Series B, Biological Sciences 200, 441–461.Google ScholarPubMed
Zhan, X.J. & Troy, J.B. (2000). Modeling cat retinal beta-cell arrays. Visual Neuroscience 17, 23–39.CrossRefGoogle ScholarPubMed